Network Drivers
Except for this brief area linking to the other section, Network Drivers are found in the Drivers section of this site, rather than the network software section.
Communications Protocols
Networking protocols: IPv6, IPX, VPN, etc.
Web Browsers
Web browsers. For more options, also see Web Editors. (Currently Web Editors are on the Web Browsers page.) Some web browser plug-ins are currently on the Web Browsers page.
Web page editors

At least some of these editors tend to not automatically do a bunch of reformmating of existing HTML.

Remote Access Tools (a.k.a. RAT)
Terminal based
SSH, telnet, modem-based communication terminal software, etc. (Servers such as BBSes, and related tools like "Door" programs.) (See also file transfer programs: TXZM has a terminal.)
Screen based RAT
VNC
File transfering programs
One can also see web browsers above. FTP, SCP. Web mirrors. wget. Bit Torrent. Also protocols that were used with modems before the Internet became big, such HS/Link and Z-Modem and source code for them. Sometimes such protocols were supported internal to terminal software (see above section). The MS-DOS Utilities (OLDDOS.EXE) for Win95 contain the MS-DOS networking software that was included with MS-DOS 6.x (InterSvr/InterLnk). There are other options to transmit over a parallel/serial port.
Chat programs
IRC, talk, various IM clients. Also, hyperlinks to send SMS may become available here.
E-Mail
Electronic mail
VOIP
Interacting with telephone network system, or not
Multimedia, games
Find such software, such as media players that download media, in the separate sections: Multimedia software, Games
Dynamic Configuration
For a DHCP hosting software for Windows, see TFTPD32 (a TFTP server that also can act as a DHCP server).
Major online service providers
Some major online service providers developed special software for integrating with them. This made a lot of sense in the days before the widespread use of the Internet, because end users needed some way to interface with the resources provided by such companies. In modern times, the usage of standardized software is generally superior than customized software which may be designed to assist the service providers at the expense of end users. For example, one company has been known to cause their software to report to end users that it was updating, when the reality was that the updates being downloaded were simply new advertisements that would be stored in a cache so they could appear quickly later.