Simple games, or complex 3D ones like HL, WOW, or Q3? They have colleges geared towards the gaming industry, that is an option to look at. You could always apply to one of the gaming companies, maybe as an intern.
Another way to get experience and possibly get into the industry is to make a mod for an existing game. You are working on your own time and money, but it could help. I've seen some mods that have become popular enough that the developers start getting approached for paid game programming positions.
well, just google search a game and the word mod, maybe you will get lucky. I don't really know many games that can be modded, but I do know that Half Life, Half Life2, and UT can be modded.
Another idea, which might be better, is to search for mods that are already out there, and try to join up on the development team.