I'm far from knowledgable in the field, but I did a survey some time ago and think these items should provide a decent basis:

Dijkstra and A* Pathfinding, Finite State Machines, Decision Trees, Hierarchical Task Networks (SHOP, etc)

Keep in mind that game ai algorithms are all about decision taking, there's little "intelligence" involved, unlike the broader aim of "general" ai.

Current game ai is vastly different than this I think. I think there is a good writeup on the ai from FEAR that might be a decent read

gameaibook.org