Backup
Cobain Backup - a free backup program that you can fully customize - scheduling, backing up to various drives including network drives, differential or full backup, etc. Uses Shadow Volume Copy so you can back up while you work on your computer. In the task pane it now also shows the total size (GB, MB...) of your backup task.
Browser
Firefox - Still the best browser. Faster than ever. Better memory management. More secure and stable. Tons of extensions to meet your needs. Check out Personas - an easy way to dress up Firefox. Now also available for mobile Android devices.
Clean-Up
CCleaner - great for cleaning up temp files, temp files leftover from crashes, and cleaning up the Registry, disabling unnecessary start-up items, cleaning up IE add-ons, scheduled events and more.
Thunderbird - an 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, and much more stable than Outlook, Outlook Express, or Windows Mail/Windows Live Mail programs. Tabs, excellent search function, File-Link (large file management) and more.
Entertainment
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...). Great for doing live mixes as you can queue songs up.
Freemake Video Converter - With video collections moving to hard drives away from disc collections, here is a great free program that you can use to convert your DVD movie or TV show into an AVI file (or other digital format). Here is the short how-to video for this process. To go with this, here is a decryption program - DVD43 - that operates in the background. It should work with most DVDs.
VLC Media Player - for playing a wide variety of video and music files, DVDs, and streaming. When Windows Media Player won't play it (WMP in Windows 7 works much better but there are still files it won't play), this will. The user interface isn't that pretty, but it works.
uTorrent - the best little torrent program around. Pronounced MOO-torrent (as the initial u is actually the micro symbol). Although there was a threat to stick ads in the free version, they backed down and made them optional.
Productivity
EssentialPIM - A personal information manager. Similar features to Outlook (outside of the email part). If you want a PIM that is not bogged down by the email part of Outlook (and it's other issues) - just a basic appointment calendar, contact list, To Do list and notes - this is a great program.
Security
AVG Free - anti-virus and anti-spyware and more, and continues to improve. Easy to use and works better than the big commercial programs. Go here for installation instructions for AVG Free 2013.
Malwarebytes - A good anti-spyware removal program to use along with your regular security program to occasionally check for bugs. Has a quickscan mode that takes about 10 minutes, and a full scan mode. Also adds as a context menu so you can right-click on a file/folder/drive and choose to scan it with Malwarebytes.
Mailwasher Free - filter out Spam before it gets to your email program. Works with a wide variety of email programs. Free version only works for one email address. Paid version will work with multiple addresses.
Utilities
7zip - 32bit or 64bit - decompression and compression of many many compression formats. After installing, run 7-Zip File Manager program as administrator, go to Tools, Options,click on the two + buttons, Apply and close the program.
Adobe Reader - Although it's big and sometimes annoying, this is still the best all round PDF reader. Works well in browsers. (I used to recommend Foxit Reader, but it is kind of buggy when dealing with opening PDFs inside a browser)
Crossloop - enables you to remotely connect to another computer to give or get help. Very simple to use. No need to create an account.
Dropbox - Actually a service, not a program, but very useful. Need to share or sync files with yourself or others in your group/business remotely, or, want to backup your work on-line? Free account starts at 2GB. There are other on-line free storage services, but Dropbox is probably the easiest to use and most versatile (and the least buggy).
From Wikipedia: Dropbox is a file hosting service operated by Dropbox, Inc. that offers cloud storage, file synchronization, and client software. In brief, Dropbox allows users to create a special folder on each of their computers, which Dropbox then synchronises so that it appears to be the same folder (with the same contents) regardless of the computer it is viewed on. Files placed in this folder are also accessible through a web site and mobile phone applications.
You can also share a file with someone who does not have a Dropbox account. To do this: Open your Dropbox folder. Open the Public folder. Right-click on the file you've put in there, select Dropbox, Copy Public Link. Then, send this link to the other person. This is a great way to send a file that is too large for email servers, or share a safe file that your email service keeps blocking (installation files, even when zipped, are often blocked by email services).
Honourable Mentions:
CDex - A simple program for converting CDs to digital audio files.
Freemake Audio Converter - a great program for converting digital audio files. Converts from and to many file formats.
EMDb - a free DVD/Video catalogue database program. Automatically downloads info from IMDB. I haven't used this but it looks like the best free one.
PDF Creator - Easy to create PDF files from any file - just print and select PDF Creator and it creates a PDF version of the file. You can also merge multiple files of any format into a multi-page PDF file. If you have Libre Office and only need to create PDFs of files you create with it, there is no need for this creator program.
More Programs
AlternativeTo - This is a great site for finding alternative programs (free or commercial) if you can't afford the usual expensive version, or for finding programs for very specific purposes.
Got any favourite free Windows programs for computer I left out? Add them in comments below.