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
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