In no particular order:
Firefox 3 - the latest version of Firefox is fast and very secure and remains the best with extensions of all the browsers
AVG Free 8 - anti-virus and anti-spyware, and much improved since it first came out. Easy to use and works better than the big programs that must be purchased.
7zip - decompression and compression of many many compression formats, and free!
Foxit PDF reader - now works directly inside a Firefox tab as well as on its own. Faster and with a much smaller footprint than Adobe Reader. They keep making this better with every version
Crossloop - for remote connections with clients for help/repair - free and very simple to use
Shutdown Guard - for stopping Windows Updates from automatically restarting your computer (XP and Vista)
Winamp - best free media player overall - yes it has playlists and you can use it with your ipod or any other MP3 player. Works better than iTunes and doesn't install other programs behind your back, and you can customize its many settings (file formats to deal with, whether it launches on its own or by your command...)
Quicktime Alternative - streamlined and unobtrusive version of Quicktime
Realplayer Alternative - streamlined and unobtrusive version of Realplayer
Open Office 3 - the best free alternative to MS Office. And it can open .docx files now. You can create a PDF directly from any of the programs in the suite with a click of an icon. Word processor, spreadsheet, drawing program, database, you can make it save things in MS Office format by default if you need to share documents with others have MS Office, and more.
Thunderbird - excellent email program from Mozilla (same group that brings you Firefox). I find this much easier to customize and to backup and move files around when need be than Outlook or Outlook Express.
Picasa - a good, free program from Google for viewing, sorting and editing your photos and more
Superantispyware - A great 2nd program for manually scanning your computer after AVG Free 8 to catch and fix anything that might have been missed. I like this better than Ad Aware and Spybot put together.
CCleaner - great for cleaning up temp files, temp files leftover from crashes, and cleaning up the Registry and more.
Cobain Backup - a free backup program that you can fully customize - scheduling, backing up to various drives including network drives, etc.
Got any favourite free programs I left out? Add them in comments.
Happy New Year!