Favorite Free Software
Image manipulation
If you're doing bitmap-type work, such as what would be done in Photoshop, then it's tough to beat Paint.NET. For the vast majority of users, it will do anything that they would ordinarily do in Photoshop. If you need tools that cannot be found either within PDN or one of its huge numbers of free plug-ins, then you're probably doing professional work and have the money to spend on the real Photoshop. The user-submitted content and tutorials in the forums are indispensable. For instance, I learned how to make shiny rounded buttons for use on websites and in my application without shelling out money on something like Adobe Fireworks or Axialis IconWorkshop.
If you're doing vector-based graphics, Inkscape might be just what you need. While not as feature-rich as Adobe Illustrator or CorelDraw, it wins hands-down in the price department (free), and will be more than adequate for the vast majority of its users.
If 3D drawing and/or animation is your gig, then Blender is direct competition for even the big-name packages like 3DSMax. Its massive following and highly involved developer base mean that if it can't be done in Blender, it's either planned for an upcoming version or can't be done at all in any 3D software. I had a good time just going through the tutorials and was amazed at what I was able to do in such a short period of time.
Instant Messaging
Pidgin is my tool of choice for IM. It connects to MSN, AIM, Yahoo, ICQ, and maybe other networks that I don't use, all at once. You can even have multiple accounts on any of the networks going simultaneously. There are no ads, and everything just works. My one and only beef is that its installation may intimidate some users, because it requires a separate installation of GTK+ and, if, spell-check is desired, Aspell. It does handle these two separate installs very gracefully and without the user really having to know anything, but it would be better if the installer were built in such a way as to integrate all these install packages into a unified interface. Just read before clicking, apply basic common sense, and all will be well.
Document Handling
Don't look for OpenOffice.org here. I don't really care for it. If it works for you, knock yourself out. It takes a vehement Microsoft-hater to claim that it compares at all with Microsoft Office, and I can't even say that I'd prefer OOo to Microsoft Works. They need to drop that stupid .org appendage to the product name, too. "OpenOffice" is already a mouthful, and tacking ".org" onto it is unlikely to ever gain the same widespread acceptance that some products have enjoyed by adopting Microsoft's ".Net" technology in their product names. Additionally, a product that appends ".Net" is indicating that it is making use of a particular technology, just as appending " for Windows" to product names back in the '90's distinguished them from DOS software. Tacking on ".org" here just reeks of "me too but different in an effort to be geek chic" and confuses people.
Ever use a computer that didn't have Microsoft Office installed, but have a need to read a Word, Excel, Powerpoint, or Visio file? No problem! Microsoft provides viewers for all of these document types for free. Since they don't load up all the tools of the full versions, these open documents quite quickly, too. Get 'em here: Word Viewer, Excel Viewer, Powerpoint Viewer, and Visio Viewer. Don't forget to visit Microsoft Update afterward to get them patched up, just in case.
For PDF reading, Foxit Reader is unbeatable. I never knew, until installing this program, that a PDF should open just as quickly as I can double-click it. It doesn't take Foxit any longer to open a text-based PDF that it takes Notepad to open a standard .txt file, and if the PDF is graphics-laden, it's only a little slower. It also consumes a tiny fraction of a percentage of the amount of space that Adobe Reader demands on your hard drive. This one is a no-brainer. It's so good that I've recommended their for-cost software without even trying it myself (which I've gotten no negative feedback about, so I must have been right). The free version is not ad-supported or anything (but there is a tiny rotator bar pushing their other products, which is no different from what Adobe Reader gives you). Unlike Adobe Reader it has a tabbed interface. They want you to love their Reader so much that you'd be willing to pay for their PDF Editor and PDF Creator products, and they make a very strong case.
For PDF generation, I typically use CutePDF just because it's free and does what it's supposed to. I also have used PDF995 but found it beyond annoying. CutePDF installs a printer on your Windows system. When you want to make a PDF, you generate a document in whatever program you like (such as Microsoft Word), and then print it. Instead of picking a physical print device, pick the CutePDF printer. It will then make a PDF file of your document which you can then e-mail on.
Note that for editing existing PDFs or creating a PDF with fillable forms, I know of no free software. I'd be inclined to use the Foxit paid versions as listed above because they're by far the cheapest I've seen and I have no doubt they'll do everything they claim. We use Nuance's products here where I work (purchase decision on that predated me) and these things are a nightmare, causing more problems than they'll ever solve. I've used Adobe's full versions (Acrobat Standard and Acrobat Professional) in prior jobs, and while the version 8 and 9 series have fixed most of the performance and stability issues of their predecessors, they are still far too expensive.
Media Handling
Winamp really whips the llama's ass. I have no idea what that means, but they claim it and I've never head of anyone refuting it, so it must be true. What I do know is that this is the best damn media player ever. I like to put it in Windowshade mode and Always on Top and set the option for it to appear above fullscreen windows, then park it up in the top right of my screen just out of the way of the min/max/close buttons of whatever program I'm operating in. Then I jam out to my MP3s while people look at me funny. It's best known for its MP3 playing abilities, but it can easily handle video file types as well. Its default installation is substantially prettier than iTunes and much slimmer than Windows Media Player. Also unlike those two, it doesn't do its damnedest to convince you to connect up to some store and buy a bunch of DRM-infected material. If you want to veg out and look at pretty stuff, its built-in Milkdrop visualization plug-in is both mesmerizing and gorgeous. Press Alt-Enter to put it in fullscreen mode, and prepare to forget what you intended to do for at least the next twenty minutes. Although the default Bento skin is more than adequate for my tastes (although I change its color scheme), you can connect up to Winamp.com and choose from hundreds, maybe thousands of custom skins.
Ever get a media file that your computer wouldn't play? Maybe you've gotten a few that played the audio track fine, but not the video? The problem is in a missing codec (a compound word meaning coder/decoder). You're actually only missing the "decoder" portion, but that's effectively semantics. It is my firm opinion that the average user should never have to even be aware that codecs exist. For whatever reason (probably something to do with licensing), when Windows Media Player 11 installs, it contains fewer codecs than Windows Media Player 10 did, causing a lot of media to stop playing properly (including plain-Jane DVD). Now, you could go out, learn which codec(s) you're missing, find [an] install package(s), and maybe get everything installed properly, usually with at least one bloated advertisement-ridden viewing program for each install. A better solution would be to see if any nice people out there have already done any of this legwork for you without including all the bloat, and fortunately, they have. There are more than a few out there, but my preferred one is the K-Lite Codec Pack. I linked to the master distribution page, which contains Basic, Standard, and Full Editions. The "Basic" package will allow your DVD's to work again. The "Standard" package will probably handle anything else you're likely to need. If you're getting a lot of things that use the widely popular DivX or Xvid codecs, the "Full" package includes those codecs and many more. Note that no matter which package you choose, you don't need to install its included Media Player Classic. Installed codecs are immediately available to all applications on the system, so Winamp and Windows Media Player will automatically pick them up. iTunes should too, but there's always the possibility that you'll have to pay an iExtortion fee to Apple before it will utilize them.
Web Browsing
I doubt anyone here hasn't heard of Firefox, but it fits the definition of the list so here it is. I strongly reject all the hype that surrounds this product, but unlike most other equally over-hyped applications, it still manages to be a solid program after all the hype is swept away. With the 3.0 series, Mozilla finally fixed one of my longest standing annoyances with the Netscape browser and all its descendants, namely, that God-awfully UGHly interface. I normally don't even care about the visual appeal of a program, so it takes something especially bad for me to bother even mentioning it. All that's needed to make a default install of FF 3.x visually appealing for me is to shut off that ridiculous Bookmarks toolbar. If they'd fix that and copy IE's default behavior of hiding the menu bar and always showing the tab bar (the latter is settable in FF so it's mostly OK), then I'd call FF nearly perfect on the presentation front. It still has FF 2.0's memory leak problem, but if they ever fix that then I'll lose a lot of ammunition for accusing it of being over-hyped, and I like my drama.
The best part of FF and the main reason to not just stick with IE is its enormous base of free plug-ins. Indispensable plug-ins for everyone are AdBlock Plus and Colorful Tabs. If you're into web design, then ColorZilla, Firebug, and the aptly but indistinctly named "Web Developer" plug-in are must-haves. IE 8 is going to become a serious contender to Mozilla's dominance in the standards-compliance arena, but until IE can match FF in the plug-ins department, FF will continue its steady march toward universal usage.
Software/Web Development
I don't know how many people here are even interested in this category, but I'll include it anyway.
Microsoft's rise to power and its legendary staying power in the position of top-dog are truly a fascinating case study to anyone interested in the world of business. While there's no one single thing Microsoft did right or did not do wrong that is solely responsible for its success, one of its pillars has been its ongoing mantra of "Developers! Developers! Developers!" You see, long before anyone else broke free from the mentality of providing the biggest and shiniest proprietary systems, Microsoft realized that attracting as many third-party developers as possible to its system would be the indispensable formula for success. Developing for the Mac platform is onerous at best because of Apple's policies on all things Apple, and developing for Linux has a noticeably steeper learning curve. Developing for any other platform is just downright hard. I recall a technology guru once illustrating it as such: if you fill up a stadium with all the Windows and Mac software in existence, the Mac software will occupy no more than the first two rows of one section, and all the rest will be Windows. Since that time, Microsoft has made an even greater effort to reach not only existing developers, but the potential developer in anyone that even has a passing interest. I'd bet that today, the Mac software wouldn't even occupy more than two seats in comparison.
Unknown to most, Microsoft's C/C++ compiler has been free to the public for quite some time. You just couldn't get it with any sort of graphical interface. What's more common knowledge is that Microsoft has made many many many software development kits and application programming interface documentation freely available to anyone. In the last few years, Microsoft has sweetened the pot to the point that if anyone wants to develop software for Windows, there are almost no barriers.
It started in 2005 when Microsoft published Express Editions of its developer tools free for anyone who downloaded it within one year. Well before that year expired, Microsoft removed even that limitation. Anyone could download and install a free visual development tool and program in Visual Basic, Visual C++, Visual J++, Visual C# and/or Visual Web Developer and never pay Microsoft a dime in any fees or royalties, regardless of what they created. Microsoft even threw in an Express Edition of its SQL database. That in itself was a pretty big deal, but of course, most people equate "computer programming" with "hard" and "too geeky for me". Microsoft then sweetened the pot even more, by opening the Coding4Fun website and filling its Microsoft Developer Network site with tons of how-to videos to get people going. It also attracts the younger programmers with its free XNA Game Studio and its partnership with the creators of the Dark Game Development Kit to offer that product for free. For the non-game builders, there are lots of "Starter Kits" that include a great deal of pre-programmed themed material that one can just modify (and pick apart to get some hands-on training). It's too bad that access to free public hosting of ASP.NET sites is hard to come by, because some of the Starter Kits for Visual Web Developer are downright cool.
Access to all these free Microsoft tools, and a whole lot more that I didn't mention, can be found at the MSDN site. The built-in help tool is pre-configured to scan the Coding4Fun, CodeGuru, and some other popular programming sites when looking for help, so a great deal of access to knowledgeable human help is built right in. Note that the last iteration of Visual J++ was in the 2005 series. That one is still available, but its omission from the 2008 Editions was deliberate (and I doubt anyone misses it).
Microsoft's Express Editions are capable of building the same applications as even the highly expensive Team Editions, but not all the tools are there. A free IDE that provides more than MS's Express Editions but not as much as the Team Editions is SharpDevelop. It should be noted that the 3.0 edition, which incorporates the changes for .Net 3.5, is still in beta and has been for a LONG time, although they swear that the final release is imminent. SharpDevelop allows you to code in Visual Basic and C#, as well as something else called Boo that I know nothing about. It's open source, so if you want to peer inside a professional C# program and see how it's done, here's your chance.
There are two proper paths to becoming a programmer. If you don't intend to do it professionally or release any big projects, just maybe do some tinkering, then get yourself a copy of Visual Basic Express, go through some tutorials, read some articles, and have fun! If you want to get truly serious about it, and be the best programmer you can be, then your path is longer and more challenging (but possibly more rewarding). First, get a good book on assembly language (I found two in the "just take it" box at the local library). You don't have to master it or even become very good at it. Just get through the first few chapters. Get an idea for logic gating, addressing, and the like. Write your first program in hex (some say binary, but that's just showing off). It doesn't have to do much (mine just displayed the letter "a" and ended). Getting close to the metal like this will give you an understanding of how the computer works (and just how stupid it really is) that you'll not get elsewhere. After that, knuckle down and get a good grasp of C/C++. Again, you don't need to hit guru stage, just get a good idea of how the compiler works and turns your (mostly) human-readable code into machine code. After that, go on to learn any language(s) you like. Just having an idea of how machine code and assembly language works will start you ahead of the vast majority of the programmers out there. Of course, the vast improvements in compiler technology are making the advantages of that position less meaningful than even a few years ago, but you'll never regret obtaining the knowledge. Besides, if you're going to do something seriously, what excuse is there for not aiming for that top tier?
System Maintenance
The one program you should have installed on your system at all times is CCleaner. It cleans up all the garbage files on your system and does a better than average job of cleaning up the registry too (just remember to keep running the registry cleaner until it finds nothing else to fix, and remember to back up all the changes it makes and keep those backups for a while).

Awesome list...