there are loads of examples on AI. pathfinding is a good one, and there are alot of sources on the net for it.
Boids is another pathfinding-esque, group behaviour, avoidance and attraction, steering...etc. There isn't alot on the internet about it, but theres enough to get you through.
Pattern recognition, neural networks, agent behaviour, state machines (finite or fuzzy), genetic algorithms are all other examples on AI.
Search and scower the internet for some of them until you find an interest, then code like mad