Free Applications

Try downloading some of these, after all you can't complain about the price. I've marked up most with their platform, and whether they're Open Source Software (OSS).
Antivirus
AVG Antivirus (Win)
A free virus scanner with free updates. Reasonably well regarded and popular, you should definitely consider installing this on any unprotected Windows machine.
Free-AV (Win)
I've never tried this, but it looks to be a worthy free alternative to AVG.
Avast Antivirus (Win)
Likewise, another free scanner I've seen in my travels.
Browsers
Mozilla FireFox (OSS, Win/Linux/Mac)
This is a browser-only Mozilla distribution with tabbed browsing support, popup-blocking, and a huge list of 'Extensions' that add immeasurable features. It's open source, cross platform compatible, fast to render, and a lot more standards compliant than IE6.
K-Meleon (OSS, Win)
This is a native Windows frontend for the Mozilla rendering engine, a similar concept to the Galeon and Epiphany browsers for Linux. Very fast to download and run.
MyIE2 (Win)
Uses the MSIE rendering engine, but adds popup blocking, tabbed browsing, mouse gestures and many more modern features. Definitely try it if you're a stalwart IE user.
Avant Browser (Win)
Similar to MyIE2 in that it's a wrapper for IE.
Opera (Win/Mac/Linux/etc)
It has adverts, but since version 7.0 I've had to revise my opinion of this browser a lot.
Evolt's browser list
Once upon a time I spent hours and hours looking for IE4.0 for 68k Macs. I finally found it, but my search would have been quicker had I headed to this first. If it can connect to a website, they have it listed, so if you're looking for a specific version of a browser hit that link. Also visit the rest of the site which has many good web-development related articles and links if you have the time.
Chat & Instant Messaging
Exodus (OSS, Win)
An open-source client for the open-standards-based Jabber instant-messaging network. If you have a (free) Jabber account you can chat to other users and also use server-side 'transports' to add contacts from other services like MSN, ICQ etc. You can also establish encrypted connections to your Jabber server if you want. Worth a look if you're sick of bloated clients but still want to chat to many services.
Miranda IM (OSS, Win)
An open source and highly modular instant messaging client. It has 'plugins' to connect to almost every conceivable IM network on the client side, and customise its interface.
Trillian (Win)
One of the original multiprotocol messengers. A free version is still available, but I prefer Miranda over this client.
mIRC (Win)
mIRC is probably the most popular IRC (Internet Relay Chat) client for Windows. If you use IRC much (unlike me) you probably already have it :).
Editors
SciTE (OSS, Win/Linux)
My current text editor of choice. It is hard to set up, requiring you to edit a configuration file, but is blazingly fast and has good tab support and syntax highlighting for a huge number of languages.
Metapad (Win)
This is extremely fast and about 50k to download. I overwrite Notepad.exe with Metapad.exe on my system and haven't looked back. No syntax highlighting or tabs; just plain powerful text editing support.
Arachnophilia (Win/Java)
I used to use this to maintain my site. It has full HTML tag highlighting and supports multiple files and an internal preview window for web pages, as well as a whole load of macros. (The name? 'A love of webs' :).
NoteTab Light (Win)
A free, very full-featured program. It supports just about anything you could conveivably want to do to plain text, and a little more besides -- however, it's slightly slow to load. Multiple files can be opened on 'tabs', instead of separate windows. Unless you pay for it, there's no syntax highlighting, but it includes an extensive scripting language. There's also
Editpad (Win)
Another multiple-files editor with a free 'lite' version.
First Page (Win)
This is a semi-automated HTML editor, with many built-in construction and preview functions. It's free, and popular acording to their download figures. I prefer smaller lightweight text editors, so I haven't used this myself, but you might be interested in giving it a trial.
There's also VI and EMACS, but I'm steering well clear of that debate :). If you have heard of them, you probably already use one or the other.
Firewalls
ZoneAlarm (Win)
One of the leading free firewall applicatiosn available (a 'Pro' version is also available). For casual users, is an application-level filter that can deny or allow internet access for specific applications. Whilst the free version is lacking in some aspects like port filtering, it's a halfway decent free firewall. I used to run this, but haven't used it for years now.
Kerio (Win)
Another firewall vendor that offers a Personal edition; I have yet to try this.
SyGate (Win)
Likewise, another free firewall.
Games
Soldat (Win)
OK, so it's not an application, and the latest versions are now technically shareware instead of freeware, but it's a great game nonetheless. Think of a cross between "Worms" and "Counter-Strike", with great multiplayer support, and a refreshingly simple story: 'A couple of guys decided to kill each other and you can be one of them'. Runs well on older computers.
Graphics
The GIMP (OSS, Win/Mac/Linux)
No, this isn't what you think. A Linux stalwart, the 'GNU Image Manipulation Program' has been ported over to Windows and Mac! It's worth it simply for the huge number of filters and effects offered, putting Paint Shop Pro to shame. The interface can be tricky, but it's highly reccommended.
IrfanView (Win)
Halfway between an application and utility, this is an excellent freeware graphics viewer. It supports operations like resize and filtering on images, and a massive variety of formats. Best of all, it's got neat 'batch' capabilities if you've got a few hundred images that need tweaking. Give it a try...
Office
OpenOffice (OSS, Win/Linux)
Well, this open-source product is just like Microsoft's Office, only free. It can work with MS Office files, and pulls all the standard tricks like underlining misspelled words and so on. With text document, spreadsheet, database, graphs, formulas, and image support, it's very comprehensive and worth a look.
Webservers
Apache (OSS, Win/Linux/Mac)
The standard. Yes, it requires some configuration, but setting this up on your home computer is a useful setup if you want to get into serious and/or CGI development.
AnalogX SimpleServer (Win)
A 250k web server that you configure by dropping an HTML file into its window. A very quick and easy way of testing out sites 'online'. Has CGI support according to its feature list, but doesn't seem to run PHP/Perl/etc. well.