AlephOne - Engine for running Marathon Infinity, 2 and 1. Has excellent network play (has improved greatly over the years) Can be tough to set up your router to act as a host though.
http://source.bungie.org/
Civilization IV demo - Cool game nice graphics, runs good. Would like to own it even though these games are usually hard for me to play or stay into (seems to take longer as it goes along) There's a demo try it out.
Droid Assault - Awesome shooter game with tactical elements from an Indie type developer. Minus is there is no multiplayer. Still probably wouldn't mind paying 20 bucks for the full version.
http://www.puppygames.net/droid-assault/
Eve Online - Minus, expensive. Plus, runs pretty good on the AMB, highy in depth with great graphics, can be time consuming if you know what to do in the game, if you don't know what to do in the game then it probably won't be too time consuming though.
http://www.eve-online.com
Myth II - One of the best strategy games ever made. In depth, highly tactical, has multiplayer. Can be tough to find a copy and possibly set it up though.
http://www.mariusnet.com
Flatout 2 demo - Only played for about 30 secs so far but has nice graphics and runs good on AMB 2.4 ghz
NetHack - Runs in Terminal, an ASCII based game of dungeon crawling.
http://nethack.alt.org
Full Tilt Poker - Poker, real money or fake, fake money tournaments can be fun
Weird Worlds demo - Awesome adventure game, single player, quick fun.
World Of Goo demo - Ok
Sky Fighters 1945 - Fairly realistic feeling (in my ill-informed opinion) flight sim. Some of the ground graphics are kind of ugly though.
FreeCiv - Civ game that is free, has multiplayer but I don't play this often.
Pox Nora - Strategy game that has a mix of turn based strategy and card trading. Can be stupidly expensive to play competitively, free to play if you just want to use the basic decks. Can be fun.
http://www.poxnora.com
Jin (chess) - A chess client I use to connect to FICS (Free Internet Chess Server)
http://www.freechess.org/
Escape Velocity Nova - Sort of a 2d single player version of Eve Online. Well not really but functions as an awesome free roaming RPG. Really wish it had multiplayer to go with the nice clean graphics. Could have servers where games last a few months and support up to a few hundred players. But no it's not to be. Maybe let Ambrosia know you would like to see that.
http://www.ambrosiasw.com/games/evn/