I'm always happy to put in a plug for the tools I use every day. With the exception of the Anti-Spyware category, all of the following software is not only free, but open source as well. You might have heard of, or even use, most of these programs already, but give the list a scan for any hidden gems you might not have encountered before.
Organize your applications over several virtual Windows desktops. In this "once you've tried it, you can't live without it" category, we have two strong contenders: VirtuaWin and Virtual Dimension. The latter application has some extra features, but it's a virtual (sorry) tie: you can't lose trying either one of them. [Windows Only]
7-Zip can create ZIP, GZIP, BZIP2 and TAR archives, and can unpack RAR, CAB, even your old LZH and ARJ files. And the Windows version integrates into Windows Explorer. What's not to like?
I am always happy to put in a word for my favourite Unix server operating system, FreeBSD. While GNU/Linux may have better support for bleeding-edge hardware, I find FreeBSD more stable, scalable, secure and usable. When you consider all the various Linux distributions out there, the fact that there is one FreeBSD is, frankly, less confusing. The excellent ports system and the fact that FreeBSD can run Linux binaries are icing on the cake.
If you need to run a particular X application on Windows, or if you prefer xterm to putty, you need Cygwin/X. It's a large download, and there are decent commercial alternatives in this category, but this is my pick. [Windows Only]
Yes, Firefox is slowly but surely winning the browser war, so I don't need to plug it a whole lot. Thunderbird will probably do the same thing to Outlook eventually, once more people try this full-featured (spell-checking, address book, spam filter, etc.) email client that provides the same slick email interface whether you're running Linux, Windows or OS X. Highly recommended.
Clam AntiVirus is a GPL virus scanner, with several interfaces (command-line, milter, on-access, etc.) and a nifty Windows interface called ClamWin that integrates into the Windows Explorer. If you think you need more virus scanning goodness than this, you should think about where you are getting the rest of the stuff you run on your computer.
Unfortunately, there are no open source products in this category, but when your relatives ask you to "fix their computers", you will probably need these. Between Spybot - S&D, AdAware SE and Microsoft AntiSpyware, there is no clear winner in this category. There's also no reason not to install and use them all -- they tend to complement each other very well. [Windows Only]
We can't have Anti-Virus and Anti-Spyware categories without dealing with Spam, can we? If it wasn't for SpamAssassin, we would have to change email addresses on a quarterly basis.
The logfile analyzer AWStats generates graphical statistics reports for web, streaming, ftp or mail server access. What did we ever do without it? Seriously, I can't remember, but it must have been horrible.
Which one is best: MySQL or PostgreSQL? The debate rages on, but the two have recently come much closer in terms of capabilities, with MySQL playing catch-up in terms of features (stored procedures, triggers, views, etc.). It's getting tougher and tougher to pick a winner, but I think they each have their strengths and appropriate place, and quite honestly, I'm as happy as a clam using either one.
If you need to securely transfer files between a Windows client and a remote computer running SSH, and you want a GUI interface, FileZilla will make your life easier. [Windows Only]
If you ever require an IRC client, you may as well use the same one on every platform you work on. XChat runs on Windows, OS X, GNU/Linux, *BSD, Solaris, HP-UX, etc. What, no PDP/11 port?!?
If you know what a text editor is, you probably already have a favourite, and if past experience is any guide, you probably will use it exclusively the rest of your days. The one they will pry from my cold, dead fingers is Vim.
VNC is, of course, the handy software that allows us to connect to and control a remote computer using the local monitor, keyboard and mouse. Usually a Windows computer is somewhere in this equation, typically the receiving end. When I need to fix a Windows computer for someone without leaving my desk, I use TightVNC, which optimizes the VNC protocol and adds several useful features.
If you work on Windows, but need to access remote Unix accounts, how can you not already love PuTTY? If only they would finish the Mac OS X port, I could die happy. Until that day, I'll use iTerm on OS X, if only for the tabbed windows. In conjunction with either of these terminal emulators, I could not work without GNU Screen, a console window manager that allows you to run interactive shells in multiple virtual terminals.