File systems for hard drives
These file systems are generally meant to be allow for reading and writing in real-time. (There are some exceptions with the "read-only" compressed file systems.) Networking file systems might go in the Network Drivers or Networking software (file transfering) areas, or here.
FAT file system types
Since the prominent operating systems using FAT as a key supported file system, during the days when MS-DOS was a supported commercial product, required that the partition tables be defined before they were formatted and used, some software to modify such partitions are in the Pre-Boot software: Partition Modifiers software area.
Basic/regular/simple/vanilla FAT (FAT12, FAT16, no long filenames)
DOS support
Q69912 says "MS-DOS began supporting hard disks in version 2.0."
Windows NT/2000/XP support

Q118335 states that Windows NT 3.51 supports 4GB FAT16 partitions. Q310561: Maximum size of FAT16 in Windows XP is 4GB arising from the use of 64KB clusters, citing that Windows 2K and NT 4.0 support this as well.

Windows 2000: Maximum Volume Sizes refers to compatibility issues with FAT16 partitions over 2GB. (This is actually referring to Microsoft Software, as noted in Q290705.)

Larger sector sizes
Overview of cluster sizes with various operating systems (also covering FAT16 and NTFS) shows that FAT16 can get to be up to 16GB if using sector sizes of more than 512 bytes.
Other operating systems
OS/2 behaves similar to DOS, having support for FAT and assigning drive letters. Other operating systems like Linux and the BSDs tend to have support for FAT that supports the LFN (long filenames), storing long filenames in a method compatible with Windows 95. This LFN support can generally be disabled (I would think... at least it can in OpenBSD.)
Long filename support
Windows 95 introduced a method of storing longer filenames on FAT partitions than what MS-DOS 6.22 or any earlier version supported. DOSLFN, DOSLFN (newer versions anyway don't work with MSCDEX.) Requires 386+. Older version that works with MSCDEX (found from link's section),

LFNDOS,

forum post,

LFNTools (in English) (Auf Deutsch (German))

author: Ortwin (Odi) Glück LFN
FAT32

Q314463 states that files that are 4GB or later won't work on a FAT32 partition.

Overview of cluster sizes with various operating systems (also covering FAT16 and NTFS).

Copy2GB has some operating system fixes for buggy handling of files over 2GB. MDGX ME Unofficial patches (search for "2-4 GB Files Errors KERNEL32.DLL") MDGX 98 Unofficial Patches (hyperlink goes elsewhere on same page, and same search string to be used), 2GB in Win2K

Others
FAT+
What used this? Is FreeDOS developing this, as seen on a Wiki? I know some Wikipedia page mentioned FAT+ and linked to the main FAT page which had no detail on it.
FATX
Used by the first Xbox video game system.
Atari Gemdos
OpenBSD 4.0's mount_msdos man page (and earlier versions, but not later ones) mentioned a -G option, saying "The differences to the MS-DOS filesystem are minimal and limited to the boot block." This was removed by OpenBSD 4.1's release: mount.h history reported: "Nuke GEMDOSFS. Unused part of unused atari port. Simplifies MSDOSFS code. Eliminates -G option to mount_msdos. \r\r Nit detection by gwk@, tom@, jmc@. \r\r ok weingart@ tom@ thib@ dlg@ deraadt@" Several other files had this same comment from the OpenBSD source msdosfs directory, at least including bootsect.h, bpb.h, and fat.h.
NTFS
Some read-only options. Paradox/Paradigm/Psomething has writable drivers for sale. (They also made some DOS, PTS-DOS maybe?)
HPFS
Read-only drivers for DOS, and at least one that writes (but is limited/shareware, only allowing a certain amount to be written at it times out, and I think it uses more memory).
ext2, ext3
Basically, as I understand it, ext3 is a superset of an ext2 drive: An ext3 driver will read ext2 drives directly. An ext3 driver will also have support for journaling or something like it. An ext2 driver can also use an ext3 drive, but it will ignore this sort of extra journaling-like features, which can cause problems when an ext3 driver later tries to access the same drive, because ext3's journal exists but it wasn't properly taken care of by the ext2 driver.
ReiserFS
ReiserFS v3, and v4
Compressed file systems
I think I made a list somewhere else. Maybe the archivers page?
Regular (read/write) comperssed volumes
DoubleSpace, DriveSpace
At least one file is available from the MS-DOS updates section. A key feature advertised for the MS-DOS 6.2 upgrade was the Data Protection Technology, DoubleGuard. (Referenced in Why Step Up to MS-DOS 6.22, more information available by running Help DoubleGaurd.) Therefore, the software from MS-DOS 6.2 or 6.22 is recommended over using MS-DOS 6.0.
Stacker
Stacker has been included in DR-DOS and IBM PC-DOS. It also was a stand-alone product. Some Stacker issues with MS-DOS: Q107526 105829 Settlement review
SuperStor
...
Read-only compressed file systems
There are a few (for Linux)
Disk Overlay software (DDO Dynamic Disk Overlay?)
(I believe this might be what this type of software is called.) Some hard drives have a boot sector which loads code that causes other hard drive data to be read differently. This code, supplied by hard drive manufacturers, successfully worked around issues of some systems with an old BIOS that could not read the data from the entire hard drive without such help. The problem is, though, the hard drive's contents could generally only be used when such software was loaded, which wouldn't be the case when one doesn't boot from the hard drive, either because of booting from a CD, or booting on a different hard drive (perhaps after the only hard drive became a secondary/slave hard drive), etc. As I understand it, the amount of memory this software took up was minimal but real, and incompatibilities could exist with some operating systems. Therefore, it is recommended to avoid using the DDO software if possible. At least some modern free operating systems support reading from drives with at least some DDO software (regardless of whether the drive was booted directly or not).
[#optdscfs]: File systems commonly used with optical discs

This has separate sub-sections for CD-based file systems and DVD-based file systems. There may be some overlap: For exampel the CD-based file system ISO 9660 may fairly commonly be used with DVD media, so check out multiple sections as appropriate.

[#cdfs]: CD-based file systems

This section is about software related to acting as a driver for CD-based file systems. For some related topics, such as lossless compression specific to ISO 9660 images, see archive-handling software: CD images area/archive-handling software: Optical disk images area for information about creating and otherwise manipulating such files. For working with DVDs in a method other than just using ISO 9660, see DVD file systems. For reading audio data from an optical disc, see the multimedia software page: section.

Common file system types:

Overview of the formats that may be supported
Simplified ISO 9660
The most basic CD file system understood by most platforms that use CDs is ISO 9660 (or actually a simplified version of it, as mentioned on ISO9660 Simplified for DOS/Windows, mirrored locally as iso9660/simpliso.htm)). (ISO 9660 features like sectors that aren't 2048 bytes big, and especially file systems spanning multiple disks, are not commonly supported.) Strictly, ISO9660 allows only for filenames that have uppercase letters, digits, underscores, and a period somewhere other than the beginning or end of the filename, and directories have the same limits except they cannot use periods at all.
Joliet file system
(mkhybrid's documentation capitalizes the name, calling it JOLIET. Wikipedia's ISO 9660 page doesn't.) Supports storing an extra copy of filenames up to 64 Unicode characters in length. Supported in Win95 and later. For another method to support long filenames, see Rock Ridge.
Hierarchical File System (HFS)
This is the antive file system used on Macintosh computers. mkhybrid is a version of mkisofs that supports making an ISO9660/HFS hybrid CD. There are other Macintosh formats that mkhybrid supports as well: mkhybrid manual (Macintosh File Formats section). The Apple Extentions to ISO9660 are an alternative to HFS also suppoted by mkhybrid. HFS supports any character except a colon (which is used as a directory separator, like \ in DOS/Windows and / in Unix), as documented in Technical Note FL36: Apple Extentions to ISO 9660.
Rock Ridge Interchange Protocol extentions
Method of preserving longer ASCII-coded filenames and Unix-style attributes (permissions, also block and character devices). (For another method of storing long filenames, see Joliet.) mkhybrid will create uppercase filenames (at least for the ISO9660 names), I wasn't very clear if this supports lowercase filenames. mkhybrid does supprot creating a TRANS.TBL file in CD directories.
UDF
See UDF overview.
[#eltorito]: El Torito
A standard affecting how CDs store bootable information and/or how they act when booted. Further details may be placed here and/or in the Archivers page: Optical Disk Images area.
ISO 9660:1999
A newer standard improving on various restrictions. This is readable in Windows XP, but apparently not Win9x. (Not sure about NT4 or 2k.)
Older standards
High Sierra Format (HSF) was considered insufficient so ECMA-119 standard was made and later adopted as ISO 9660.
File system drivers:
[#cdfsdos]: Drivers for MS-DOS and compatible operating systems

These file system drivers need to know which CD Drive driver for DOS has been loaded. The way to determine the drive is to specify a name which is set by the CD Drive driver.

Sam Houston State University Compact Disc Extentions (SHSU-CDX)
SHSUCD15

shsucd15.zip contains the SHSUCDX 1.4b executable as well as other programs (apparently designed to create and work with CD images).

This does not have a newer version of SHSUCDX than version 1.4b, but does contain a newer version of SHSUCDHD. SHSUCD14.ZIP contained an older SHSUCDHD 2.0 (as can be seen in the SHSUCDHD.ASM, SHSUCDHD.EXE, and README.CDH files, even though README.CD errorneously indicated the SHSUCDHD version was 4.0.)

Other versions
Version 3 has support for an 8086 again, unlike version 2 which required a 386+. (Version 3's SHSUCDX.EXE still requires a 386+, but it now comes with a SHCDX86.Com.) This supports the CD-ROM extentions for DOS like MSCDEX does. I have noticed this not working as well with MSCDEX (if I recall this right, it was an old version, 1.4b, which would not play CD audio on a system's second CD-ROM drive if a specific CD drive was loaded with the Config.Sys... Results were different with a different CD driver or if MSCDEX was loaded.) Fortunately, SHSUCDX supports a /U option to unload itself. If it doesn't work, one could try MSCDEX as a backup. Version 3.04's readme cites problems with using a version of DOSLFN earlier than 0.40a. Locally, several files have been zipped together into one olderver.zip.
Microsoft CD-ROM Extentions (MSCDEX)
At some point, MS-DOS started coming with MSCDEX. Version 2.95 comes with Windows 98 Second Edition. Version 2.23 can be downloaded from Microsoft, meant as an update for earlier versions of MS-DOS. (See MS-DOS updates.)
Novell (Netware) version
As I recall, NWCDEX.EXE used less memory than MSCDEX.EXE. See information by Caldera OpenDOS and/or DR-DOS 7.0x. (For now, see DOS versions for any relevant details on this site.)
CORELCD.EXE
Mentioned in Wikipedia ISO 9660 article, and some other articles on the Internet as an alternative to MSCDEX (as an ISO 9660 driver for DOS). (TOOGAM has not found any other information on this.) Presumably (although TOOGAM has not verified this) released by the same company that is famous for making CorelDRAW.
[#wn9xcdfs]: Win9x
Alternate CDFS.VXD (created by cyber7)
Alternate CDFS.VXD (created by cyber7) (zip of alt CDFS.VXD) Win95/98 Driver that let's audio CD's be seen as data files, and songs get copied when the "files" shown by this driver get read. To install: Backup and then overwrite %windir\System\IOSubSys\cdfs.vxd with contents of zip file, then reboot.
Handling image files
Mounting CD image files in Windows
*.ISO file systems can be mounted by some virtual drives. Because these pieces of software do not just appear as a mounted file system, but also as a CD-ROM drive (visible in the Device Manager, which can have properties such as reporting whether the disk's tray is opened or closed), they are being treated as virtual drives. More information can therefore be obtained from the Drivers for Compact Disc drives page.
Making/modifying/extracting-from CD images
See the File Archiver page.
Macintosh
Joliet
Joliet File System for Mac OS 7-9
Rock Ridge
For "systems before MacOS X," which "cannot manage Joliet and Rock Ridge filenames", there is Joke Ridge.
[#mntcdunx]: Mounting optical discs in Unix-like environments

Mounting an actual optical disc from a drive is rather straightforward and easy once one is familiar with how to mount other file system volumes, such as the ones storing information on a hard drive, and once the CD device is known. To check the name of the optical drive, try using:

ls -l /dev/*cd*

If that turns up only one result, that is probably it. If it turns up many results, consider narrowing it down to:
ls -l /dev/cd*

If there are multiple /dev/cd* with different numbers (such as an OpenBSD default install continaing /dev/cd0a and /dev/cd0c and /dev/cd1a and /dev/cd1c) and only one optical drive, the desirable block device to use is probably one with the lowest number, a /dev/cd0? in the example given.

(In the above example, dev/cd0c is the desired device. Using the entry that ends with c is similar to how OpenBSD handles partitions on a hard drive, something one generally learns when installing OpenBSD and learning how to make a proper disklabel which other operating systems may refer to as a bsdlabel.)

If a /media or /mnt subdirectory exists and a *cd* subdirectory exists under one of those things, that is probably meant to be the mount point of a CD.

The mount command will need a -t parameter which is not consistant. If the optical disc uses UDF, try -t udf. If the optical disc uses ISO 9660 CDs, the parameter may be -t cd9660 or -t iso9660.

Specifying “-o ro” is generally unnecessary. Specifying “-o ro,unhide” is generally unnecesarry. One exception is the WoW:WotLK UDF DVD when used under Debian. However, using -o ro,unhide in other operating systems my not work (citing “unhide” as an unsupported, invalid option).

So, an example of all this may be:
mount -t udf /dev/*cd* /media/*cdrom*
echo Note that the above may need customizing.

Additionally, support is generally included in the operating system to be able to mount *.iso images. However, most operating systems which support this functionality will require an additional procedure, not just mounting a *.iso image directly. (I believe this might not have been true with some older versions of Linux.) The secondary procedure may involve creating a vnode device with a separate command (and then, to cleanly free up resources, un-creating that device after unmounting the drive), or an altered mount command. See: Mounting disk/disc images in Linux, Mounting disk/disc images in OpenBSD, and Mounting disk/disc images in FreeBSD.

[#mntimlnx]: Mounting disk/disc images in Linux

Support for mounting images is built into standard Linux distributions. The syntax may be mkdir /mntpoint;mount -o loop -t iso9660 filename.iso /mntpoint

[#mntimobs]: Mounting disk/disc images in OpenBSD
OpenBSD FAQ page 14 - Mounting disk images in OpenBSD discusses mounting a disc image with built-in software. One can mount with vnconfig svnd0 filename.iso;mount -t cd9660 /dev/svnd0c /mntpoint; and can unmount with umount /mntpoint;vnconfig -u svnd0
[#mntimfbs]: Mounting disk/disc images in FreeBSD
FreeBSD 5.x and newer
mdconfig -a -t vnode -f filename.iso -u 1
The -u 1 above causes /dev/md1 to become mountable. (Use mount -t cd9660 /dev/md1 /media/cdrom ).
To undo this, umount /media/cdrom and then use:
mdconfig -d -u 1
FreeBSD 4
In FreeBSD 4.x, mount with two commands:
vnconfig /dev/vn0c ./image.iso
mount -t cd9660 /dev/vn0c /cdrom
Umount with a standard umount /cdrom followed by:
vnconfig -u /dev/vn0c
This whole process is similar to OpenBSD's, and is noted at The FreeBSD Diary's page on mounting an ISO image.
[#dvdfs]: File systems used on DVDs
Quick overview

Note that some older operating systems and/or implementations of file systems may not be able to store files that are over 4GB. Archivers (and archive formats) may have limits, such as noted by the Info-ZIP documentation of zip 2.x zipfile specification's archive limits do reference 2GB and 4GB limits. Of course, numerous other file size limits may go into effect (like the 504/540MB barrier that some BIOS codebases inflict upon hard drives), but this is courteously mentioned since working with full-sized DVDs will exceed some of these limits that often don't affect other tasks.

DVDs most often store data in one of the following methods:

[#udfovrvw]: Universal Disk Format (UDF)

UDF is used by some removable media, included DVDs. Wikipedia's article on UDF says "Almost directly after the first version of UDF was released, it was adopted by the DVD Consortium as the official file system for DVD Video and DVD Audio. Nowadays, a UDF file system may be found on most authored optical discs in the market, and on almost all recordable DVD media that are used for video recording." UDF may be supported on more devices than ISO 9660. For any further details available here, see #udf section.

CD-based file systems
CD-based file systems, such as ISO 9660. For further information on these disk formats, see the section on CD-based file systems. ISO 9660 works with many devices that can read DVDs, and is popular since software that handles this format also is usable for making CDs.
[#dvdcrovw]: Encryption, a.k.a. copy protection

Many commercially made DVDs include some form of copy protection, preventing unauthorized accessing of the data. This prevents playback unless the data is decrypted, and so naturally they are meant to be decrypted in some fashion. That method is to use DVD Playback software. Some such software may mount the DVD file system in a way that provides access to the files in an unecrypted manner. Another possibility may be disk writing software, since such software may provide some sort of method of using such encryption. For any such details, check out the software area on writing CDs/DVDs. (Until a more specific hyperlink is available here, search the general CD software area.)

For software that provides access to unencrypted data without performing one of the above functions, the most appropriate part of the site for such a thing is the DVD encryption section below.

Unlike ISO 9660, UDF supports packet writing.

Further details

This is meant to be the area where specific files are located, in order to keep the overview areas small, so that they may be used as a quick overview.

Universal Disk Format (UDF)

For a quick overview, see UDF overview. (Not a lot of further details are currently available here.) There are various versions of UDF: See Wikipedia: Revisions of UDF and Wikpedia: Flavors of UDF. Q321640

Wikipedia: Mount Rainier (packet writing) says "The physical format of MRW disks is an extension of the UDF format"

A technology which has become fairly common and often using UDF is a DVD. Consequently, UDF may be supported similar to ISO 9660 by the same sort of software that handles CDs. For example, in Unix the mount command may simply need a different option (using -t udf). To write to a DVD, software that handles CDs may also have support for using DVDs storing data in ISO 9660 or UDF format. (However, in Unix-like operating systems, CDs are generally written with cdrecord whereas DVDs are often made with growisofs.) Consequently, information on handling DVDs may be in this site's section of handling CD-based file systems, possibly with a quick note of UDF-specific information.

CD-based file systems
CD-based file systems already have their own separate section, and so details are located there, in the CD-based file systems area, and not here in the DVD systems area.
[#dvdcrypt]: Encryption, a.k.a. copy protection
There is not currently an abundance of such software on this site. What little information that is available is covered by the overview.