A great way to start is by forsaking graphics altogether and making some text games. Making a text RPG, for example, can be rather simple, or it can be rather complex, if you would like it to be.
If you haven't made a simple game where the computer thinks of a random number and the player tries to guess the number, that's a nice and simple one, too

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Worlds at War (Current Project) -
http://www.awkward-games.com
Ganadu'r, The Eternal Sage (Other Current Project) -
http://rpg.naget.com
Programming tutorials and web-design services:
http://www.wyrmmage.com