Microsoft Internet Explorer
In general, three things are recommended:
Internet Explorer 7
Internet Explorer 7 does not work with Windows 3.1 or any earlier version of Windows, nor Windows 95, nor Windows 98, (neither Standard/First Edition nor Second Edition), nor Windows Millenium Edition ("Windows Me"). (I believe it doesn't work for Windows 2000 either, and only supports Windows XP and newer... perhaps Windows XP SP2 and newer.)
Internet Explorer 6
Microsoft Internet Explorer 6.0.2800.1106 SP1 (local copy)
A zip file of the files downloaded on a fresh install of Win98SE (having added no third party software to the Win98SE installation other than network drivers obtained from intel.com).
Security Updates
Update rollup
KB889669: “update rollup” “for Internet Explorer 6 Service Pack 1”. There is download information for KB889669 for Win98/98SE/Me/NT which refers to download page
Latest MS IE Cumulative Security Patch for Win9x
MS06-21 / KB916218 appears to be the last Cumulative Security Update for Internet Explorer that worked with Windows 98, 98SE, and Me.
Latest Outlook Express Cumulative Security Patch
The Latest Critical Updates link did point to April 2006, Cumulative Security Update for Outlook Express (911567) as the latest. Although OE is often viewed as a separate program from IE, the latest version of OE was able to be installed using the IE6 setup program, so it is hereby mentioned. However, MS06-016 wasn't made for Win98(SE)/Me due to it not being "critical". It replaced MS04-018 and MS05-030 which also didn't have Win9X versions released for the same reason. MS04-018 itself replaced MS04-013 / KB837009, and that did have a Win9X version. There are multiple releases of executables for this particular patch, depending on the OE version ( 5.5SP1, 6.0 for XP, or 6.0SP1). There was also a release from Windows Update: Windows Update KB837009 file.
Microsoft Internet Explorer 5.5x
Updates
Q314564/KB314564: “Internet Explorer 5.5 Post-Service Pack 1 Security Rollup Package” page says the package “is available in Internet Explorer 5.5 Service Pack 2 (SP2).”
Internet Explorer High Encryption Pack (MS IE 5.5 note)
To quote Microsoft's Internet Explorer High Encryption Pack page (adding the domain name to the URL being quoted):

Note: Internet Explorer 5.5 includes 128-bit encryption. If you already have Internet Explorer 5.5 installed, you do not need to upgrade your browser with the Internet Explorer High Encryption Pack. If you are running Windows 2000, installing Internet Explorer 5.5 will not change the current level of encryption on your computer, you will need to install the Windows 2000 High Encryption Pack.

The linked to page supports several languages. Win2K High Encryption Pack Redistributable Download (renamed locally as encw2aen.exe)

Microsoft Internet Explorer 5.0x
Release for 32-bit Windows
Last version to have FrontPage Express. IE 5.01 SP2 for Win32 (download page) (direct link) (local) Q261268: Description of IE 5.01 SP1 says 5.01 SP1 for Win95, 98, and "Windows NT 4.0 includes a standard 128-bit encryption strength and supports the U.S. government standard for data encryption (DES)."
Release for 16-bit Windows
Q217145 Readme.txt included with IE5 for Win 3.1 and Win NT 3.51 (may be local as q217145.htm)
Internet Explorer High Encryption Pack (MS IE 5.0x downloads)
Q195833 tells us "The standard 40-bit versions include Server Gated Cryptography (SGC) technology." "With SGC technology, international customers can conduct 128-bit transactions with banks and financial institutions (that support SGC) around the world."
MS IE for the Macintosh

Now discontinued, this version of MS IE used different rendering code (see Wikipedia: page on Tasman (layout engine)) than other versions of MS IE, and so the latest version of MS IE for the Mac displayed many web pages differently than any version of MS IE for Windows, in some cases due to superior compliance to documented standards than the Windows versions.

Getting MS IE for the Mac:

Wikipedia's page on MS IE for Mac says Microsoft "removed the application from their Macintosh downloads site on January 31, 2006." The site links to Pure Mac: Web Browsers (MS IE section) which links to MS IE 5.2.3 for Mac OS X Intel & PPC Native (download URL) and MS IE 5.1.7 for Mac OS 8/9 PPC Native ("Classic PPC") (download URL). These download URL's are simply redirectors to: MS IE 5.2.3 for OSX, from redirection, to Browsers.Evolt.org from MirrorService.org and MS IE 5.1.7 for MacOS, from redirection, to Browsers.Evolt.org from MirrorService.org. Locally, these files have only been stored zipped since storing them that way allows them to take up less than one third of the disk space, and since the files are available elsewhere.

Other release info

IE 5.0 RK Chapter 4 says the browser can be installed on "UNIX, including Sun Solaris 2.5.1, Sun Solaris 2.6, and Hewlett Packard HP-UX" "Internet Explorer supports the primary UNIX installed systems. Users can also remotely use Internet Explorer for UNIX from other UNIX operating systems, such as Linux, Silicon Graphics IRIX, and IBM AIX."

Win98SE came with MS IE 5.00.2614.3500 (with 40-bit Cipher Strength).

MS IE 4.0
16-bit release
Q184330: IE 4.01 for Win 3.1 installation info with system requirements
Internet Explorer High Encryption Pack (MS IE 4.0 downloads)
MS IE 3.0x
Info
An Old IE3 for Win16 download page describes the differences between the installations for IE 3.03 SP1 for Win 3.1 and NT 3.51. All installation packages included IE and JVM. The "Browser and Mail" packages (for 3.1, and NT 3.51) also included a Mail Client, whereas the "Typical or Basic Install" package (for 3.1) instead included a TCP/IP Stack & Dialer. The full package, of course, included all of the above. IE3SP1 notes, System Requirements (renamed sysreq3s.htm locally) http://download.microsoft.com/msdownload/ie3/sp1/win16/en/dlful30f.exe It would seem there have been multiple versions using these same sorts of filenames, including 3.03 SP1 and 3.02a. I've also seen a reference to dlful30d.exe
3.03 SP1
16-bit
http://www.devili.iki.fi/pub/browsers/Microsoft/win3/dlful30f.exe LightSpeed's making disks page links to dlful30f.exe, and to a page of alternate download locations including: dlful30f.exe, dlful30f.exe, dlful30f.exe, dlful30f.exe. Evolt.org pointed to a smaller file, which has a smaller and older iexplore.exe (according to the bundled FILES.INF files). dlful30f.exe download page http://www.mirrorservice.org/sites/browsers.evolt.org/browsers/ie/16bit/3.03/win31/dlful30f.exe
3.02
Q171066: Directory listing of the Msie302m.exe File (Upgrade Version) (and the contents of its files over 200K)
Some more info

Microsoft's updates have been listed on a page listing TechNet bullitens. Details about other updates, including older ones, have remained available for continued reference. I have amassed a collection of updates from the Windows Update site right as Microsoft was finally discontinuing support for Windows 98, Windows 98 Second Edition, and Windows Me. Hopefully they'll be somewhere in this download archive eventually.

As mentioned elsewhere on this page, the latest Cumulative Security Patches aren't necessarily the latest patches. I might have some more available in a collection of patches from Microsoft that I had made. Also, MDGX's IE updates section has links to some updates, some of which might not be packages officially created by Microsoft (but may still be good anyway). Microsoft is not releasing further updates to MS IE for Win9X. This does have the positive side that there isn't as much exposure of any remaining flaws, and it is likely that fewer troublemakers will seek out problems in Win9X to exploit as the software becomes older and used less. Still, security concerns and desires for updates may be compelling reasons to switch to newer browser versions, such as MS IE 7 on a newer operating system or Firefox 2.

More links
Some more links I had accumulated in an earlier version of this web page follow. Some of these might be redundant with what is above.
Increasing connection count
Configuring MS IE 5.5+ for multiple downloads. (Version 5.5 listed as minimum version due to Q282402.) In HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Internet Settings are (according to MS article 835821):
MaxConnectionsPerServer
Maximum number of simultaneous downloads from any one site.
MaxConnectionsPer1_0Server
Maximum number of simultaneous downloads from multiple sites.
Specified as hex when stored in a .reg file (even if you set to a decimal value in RegEdit).
REGEDIT4 [HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Internet Settings] "MaxConnectionsPer1_0Server"=dword:0000000a "MaxConnectionsPerServer"=dword:0000000a

"The previous edits can affect the stability of the HTTP protocol. Be prepared to switch them back if your browsing becomes unstable." Q282402 says "Changing the maximum number of connections beyond two is a violation of Internet standards; Microsoft does not recommend this procedure for use outside closed networks." Indeed, violating this standard has been treated as a hostile act in the Internet's early years when servers were less powerful and less capable of handling as many users: Some sites might even have banned users for increasing this. Then again, some websites would encourage this, even in the case of a paid commercial site (often viewed as inappropriate for viewing in professinoal settings) which would be harmed by slower server performance. Even Microsoft has stated, "To comply with current Internet standards (Request for Comments 2068), Internet Explorer limits the number of simultaneous downloads to two downloads, plus one queued download. This configuration is a function of the browser. However, as connection speeds increase, and the number of total connections that are allowed to Internet servers increase, the two-connection limit may be restrictive."

To set these to 10 (as per MET's "Speed of Sound" page), see execute (saving to disk if needed) this registry file (modifying the hexidecimal numeric values as desired). If the saved file ends with a .reg extention then common setups will result in RegEdit applying the settings.

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