It all depends on what kind of game AI you're interested in. Approximating a solution to a chess game is one kind of AI; running a game like StarCraft is vastly different; and a shooter is going to be different yet again.

Some techniques are good to know and will appear in various flavors in many different forms of AI. You should pick up books like Game AI Pro or the AI Game Programming Wisdom series (full disclosure: I have articles in the Game AI Pro series, although I collect no royalties for them). That kind of reference will be very valuable and give you a vocabulary for talking about game AI tools with other programmers and designers.

An AI for StarCraft can be a good exercise, but in general you'd be better served with something more original: design your own game and implement an AI to play it. Could be any kind of game, from a Mario style platformer to a Battlefield style shooter or even a strategy game.

The reason I recommend this is that game AI programmers must interact with virtually every sub-discipline within game development. You'll need to be at least passingly familiar with animation, rendering, audio, physics, and so on. The more breadth you have as a developer the better AI programmer/designer you can be.

Preach, brother Apoch!