Josh's List of Free Software Games
My Favorites
vor - Variations on Rockdodger
I helped write this, so naturally I like it. :) A simple 2D space game with basically Newtonian physics. You pilot a ship through an asteroid field. Your ship has four-way thrusters, which both move your ship and push the rocks around. The only objective is to stay alive for as long as possible.
xkobo
Another great 2D space game. Your ship moves in 8 directions, and shoots bullets out of both ends. This makes for a neat dynamic, as you can kill things by driving straight away from them. Destroy the enemy bases which are made out of pipes. One hit and you're dead. 50 levels, which repeat with increasing difficulty.
wok
http://www.asahi-net.or.jp/~cs8k-cyu/linux/wok_e.html
You control a flying "wok" with the mouse. Balls of various sizes fall from the top of the screen; your objective is to catch them all and throw them off the right side of the screen. If any ball falls off the bottom of the screen (they fall more slowly the closer they get to the bottom), you lose. Throw more balls at once for score multipliers. Simple, yet fun.
Qonk
https://sourceforge.net/projects/qonk/
Just about the simplest possible real time strategy game. It's set in a solar system, with many planets and moons. Your planets and moons produce ships, which you can send to take over other planets. The object is to take over the entire system. Games only take a few minutes.
Trip on the Funny Boat
http://funnyboat.sourceforge.net/
A simple action game in Python. Side view, you control a steamboat (which can jump!) with a small cannon. Pilot it safely through shark and pirate-infested waters, avoid the mines, shoot seagulls, and finally sink the "legendary Titanic".
Could Have Been Better
Ri-li
Drive a train around various tracks. The object is to collect all the cars without crashing into yourself. The implementation is solid (and has translations for a bazillion different languages), but the controls are rather annoying. You have to make choices at places that I don't think you should have to. This is apparently by the design; many levels make use of it to make them harder. I just find it annoying.
Great Idea, Poor Execution
Don't even bother playing these. However, if you feel like using the idea for a new game, and doing it right, I'd love to hear about it...
Rebound
http://rebound.sourceforge.net
Breakout, only you control the ball's left/right motion directly (no paddle, ball bounces off the bottom). But if you let off the arrow keys, the ball reverts to going straight up and down. How dumb is that? The arrow keys should accelerate the ball left and right, and it should have proper inertia. Neat idea, but I don't recommend actually playing this one.
Tower Toppler
http://toppler.sourceforge.net
A jump-n-run where you are climbing up a round tower. Instead of your character moving left or right, he stays in the center of the screen, and the tower rotates. Which is a neat visual effect, but the gameplay is simply AWFUL. There are (unmarked) blocks that push you to one side or another, or vanish from under your feet with no warning. There are things that zip in from the side and kill you, and depending on where you are you have zero opportunity to dodge them. They used the SAME BUTTON for shoot and jump. If you're moving, you jump instead of shoot, and you can't jump high enough to get over an enemy, so if you were trying to shoot, you generally just die. Don't even bother playing this one. But it would be cool if someone would implement something like this which was actually fun...