There are C#, Flash, Java versions if you aren't into C++. Lots of documentation on the web, but the getting started guide is good enough.
AI is often cast as constraint solving, and a physics engine is basically a constraint solver. Of course, for real the AI engine runs next to the physics engine. Ah! I should have mentioned Rodney Brooks' work:
http://en.wikipedia.org/wiki/Subsumption_architecture
where you model intelligence as a bunch of simple prioritized reflex-like behaviors. Now, on each step, you have each "entity" execute their reflexes according to the current environment, where some reflexes act to disable others. The reflexes are incredibly simple, you probably couldn't even express A* path finding, but you could have the act as ants following a diffusely scented trail. Also see his paper "Elephant's Don't Play Chess."
Custom (non-physics) solutions involve declarative sets of constraints being solved by some sort of engine; such solutions often start to resemble physics engines even if the physical rules even if the constraints are not exactly physical.
Learning how to use a physics engine, first, then how those physics engines work, is a good start to understanding these kinds of problems.
Edit: I'm really surprised the stackexchange answers don't mention this.