Compression and Backup
Anyone who actively works at a computer frequently encounters an alphabet soup of data compression formats. Names like ZIP and RAR and CAB and TAR could be the title of a Dr. Seuss book. The free and open 7-Zip utility can unpack most of them (and pack ZIP and its variants), plus it integrates into the Windows Explorer for direct file access.
Data backup is like preventative medicinewe all know we should, but few of us do. One small business recently made the news when a disgruntled employee deleted $2.5M worth of files, which had not been backed up. The data was ultimately restored, but not without shelling out likely thousands of dollars to a specialized recovery firm. You can use Windows' built-in data backup tools, or turn to more sophisticated free and open source solutions like Amanda, NasBackup, or Cobian Backup 8 (note that the newer Cobian Backup 9 is not open source).
Viruses Begone (and Spyware, Too)
Several anti-virus and anti-spyware scanners for Windows won't don't cost you a thing but they're not open source. There is one ClamWinthat's both. Although ClamWin maintains an up-to-date database for both viruses and spyware, unlike some free-but-closed-source scanners it does not monitor and scan files as you access them. Rather, you must run a ClamWin scan against files manually.
Windows includes a client for Microsoft's Terminal Services remote desktop, but not all Windows licenses include the remote desktop server. UltraVNC is a free-and-open-source remote desktop client and server for Windows that also supports live text chat and file transfer. If you use a platform other than Windows, you can connect your Web browser to UltraVNC's Java applet to view the Windows desktop.
And Firefox, Too
A special mention should be made about the Web browser Firefox, perhaps the most well known free-and-open-source application of them all.
Firefox is really one branch of a free, open source ecosystem. The browser is based on the Mozilla Foundation's rendering engine named Gecko, which is also the basis for several other free-and-open Web applications like the SeaMonkey Project (with integrated e-mail and calendar), Flock (with integrated social networking), and K-Meleon (chameleon) which is lighter and more tightly integrated into Windows than Firefox.
Thanks to the philosophy that drives open source software developers, they create new applications rapidly, often incorporatingand sometimes exceedingfeatures found in analogous commercial applications. While open source applications may fall short of your needs, they cost nothing to tryand nothing to keep.