Online Games
Radical Play: http://www.radicalplay.com/
Radical Aces is a game I really enjoy. Its a flightsim fps based on mars. These guys just made a new version of the game that is better in some ways (including gfx), but try the original one out as well. I also suggest the game Need for Madness. Its a very fun "win the race or kill all the other dudes" racing game with many levels. Apparently a new version of this is under development now that Radical Aces 2 is out. All is free (but you can pay to get a code to unlock some planes in Radical Aces 2).
MaidMarian: http://www.maidmarian.com/
There are some stupid multiplayer games here. Tankball is really the one that I like. Its fun and fastpaced. The other games pretty much suck (unless you are an rpg fan)
Open Source Computer Games
BZFlag: http://bzflag.org/
REALLY FUN fps multiplayer tank shooter. You have to try it. A nice thing about this game is that you dont have to download maps. You just log into the server and the map is downloaded for you. I have always wanted to make a world and server for this game.
Warzone 2100: http://wz2100.net/
Its a good rts. Its tech tree and modular unit design features are what make it special. Also, the campaigns are fun. The ai tends to be good too. gfx are okay, and spring users may detest the point and click interface (everything is done with the left mouse button). The user base seems to be dying, and this makes me very sad.

Nethack: http://www.nethack.org/
Dwarf Fortress was already posted here, so I had to post this. It is a wonderful dynamic rpg, with lots of great features. It is old, and used to use an ascii map (now graphical tiles are used). It has versions for every os, even Windows Mobile. This game will be a favorite for me even 50 years after its conception.
Globulation: http://www.globulation2.org/wiki/Main_Page
Its a great rts concept. Definitely needs work, but I think that it is a great new idea, and I find it fun to play now and then. I have never tried online play, and I am sure that is more interesting. Please play it just to see this interesting take on how an rts should work.
YSFlight: http://homepage3.nifty.com/ysflight/fromauthor/e.html
Great flight sim!! You can also setup custom combat situations. In these situations, it is important to use flares to avoid missiles from planes and the ground. I love this thing. Its great to fly around in a helicopter or an awesome fighter jet shooting down concords, wwii planes, or 747s. fun fun fun
Some other games I looked at but have not tried:
Hover Race: http://www.hoverrace.com/
This looks like a fun hovercraft race/battle (win the race or kill all the other dudes)
Tremulous: http://tremulous.net/
Just looks really awesome. Its supposedly a futurist team-based rpg.
Planeshift: http://www.planeshift.it/
A nice looking rpg with a good storyline
I ASSUME NO RESPONSIBILITY FOR THE SUCKTITUDE OF THE ABOVE 3 GAMES. I HAVE NOT TRIED THEM. I HAVE BEEN TOO BUSY WITH SPRING.
I really like these (the ones I tried) games. They are like my babies (even though they are not mine). Please tell me what you think!