A few that I don't see mentioned:
Image Apps:
Inkscape - A free vector graphics editor. Lots of fun to play with, similar to Illustrator or CorelDraw
Office:
Abiword - Just the 'Word processor' portion of the Office Suite idea, but much faster, smaller, and lighter weight than either Open Office Writer or MS Word.
Games:
Battle For Wesnoth - Fun, multiplayer turn-based strategy.
OSes:
Fedora - Another Linux distribution, concentrating on being pure free/open source, including a completely open development process, with a rapid release/development cycle.
SuSE - Yet another Linux distro. Not personally very familiar with it, but also well thought-of.
By the by, all of the linux distros mentioned include a 'livecd' option, so you can try them out without installing anything.
Also, as a minor nit, the OP doesn't really make a distinction between Free as in beer and Free as in Freedom.
Here's an essay that explains the difference, and why it matters.