Free Media / Audio Software

I've labelled most of these with their platform compatibility, and whether they are Open Source Software (OSS).
CD Rippers
CDex (OSS, Win)
Cdex is a 'CD Ripper' - it converts music from audio CD's to files you can play on your computer, often highly compressed. Why? Simply because most people own a gazillion CD's and lack a changer capable of holding them all. Create your own playlist of your favourite tracks, ripped to WAV, MP3 (via the LAME encoder), WMA (Windows Media Audio), AAC, VQF, or OGG files.
Exact Audio Copy (Win)
Like CDex, but focuses on very high quality rips. Has many options to avoid clicks and reading errors, and the usual encoder support.
ISO Buster (Win)
A great CD/DVD analysis utility. View the TOC data on a CD, extract tracks or sessions to image files, load/view/convert image files, build cuesheets, retrieve data from damaged CDs, and more.
Codecs
FFDShow (OSS, Win)
Don't bother installing DivX, XVid, and half a dozen other MPEG4 codecs just for playback. Instead, get this. It plays them all, and has an incredible amount of post-processing options to enhance the quality of MPEG4 video content.
OGG Vorbis (OSS, Win/Mac/Linux/etc)
Patent-free, royalty-free and high quality, this is a great audio codec.
RareWares (Various)
A collection of hard to find encoders and decoders.
Media Players
Media Player Classic (OSS, Win)
This is a replica of the Windows Media Player 6 GUI, with the internals completely reworked from scratch. It plays audio and video, with fine-grained control over codecs and filters in use, and supports almost any format with the codec installed (including WMV, Real, Quicktime, DivX/MPEG-4, subtitling, etc...). Great stuff if you're looking for a fast, free video player.
Winamp (Win)
The original and still one of the better media players. Now with video support, and a decent media library.
foobar2000 (OSS, Win)
Don't be fooled by its simple looks. This is the most customisable audio player I have ever found, with a highly modular design. Designed by audiophiles for high-quality audio processing and playback, it plays most popular open formats. If you do use it, try some of the formatting string available with the default UI.
Videolan Client (OSS, Win/Mac/Linux)
This is a very interesting piece of software. It natively plays almost any standard media format, including DVDs, and can stream files over a LAN for playback on a remote computer.
ITunes (Win/Mac)
It's out for Windows. Some people swear by it; I've never used it much.
RealPlayer and QuickTime
Gotta have them; use Media Player Classic to play them. If you're adventurous, try Googling for 'Real Alternative' and 'QuickTime Alternative', but I'm not too sure how legal those pieces of software are.
Miscellaneous
Audacity (OSS, Win/Mac/Linux)
Audacity is a great free WAV audio editor, with lots of features and a very friendly interface. Supports loading and saving many different formats, and has a large range of effects. Beats SNDREC32.EXE any day :).
GEISS (Win)
It should be under the 'Links' section really, but this site has several programs that should push your computer's graphics capabilities to their limits.
MP3Tag (Win)
Organise and mass-tag your collection of MP3, Vorbis and other audio formats. Can guess tag values from filenames or vice-versa, and retrieve information from the internet.
Peer To Peer Networks
Gnutella
Whilst not edible, Gnutella (originally by Nullsoft, who also made Winamp) is very good at creating a large distributed file sharing network. Basically, this means mp3s of dubious legality. However, since it has no central server, anything can and often has been shared - each user has to connect to another Gnutella user, who in turn knows several other users, and so on. The original Gnutella program is now pretty out-of-date, but several free replacements like Gnucleus exist. See Zeropaid for more.
KCeasy (OSS, Win)
Based on a backend called giFT, this is an interesting-looking multiprotocol P2P client.