My first "serious" program when learning a language, is a number guessing game. Where the comp gets a random number and the player has to guess it. The comp is guiding the player in the right direction by telling if the number bigger or smaller.
When I'm comfortable enough around a language, I create a Reversi game.

I want to participate in this competition with a Reversi. I'll do it in Python an Qt, and call it PeQersi. Wanted to do it for some time and this competition will be a good motivation.
I started working on it, and it's about 10 percent finished.
Didn't put it up anywhere yet. Want to reach a player vs player gaming level of script, so people can use/test it.