I have always wondered if the animation technology used in film-making uses AI to any extent.
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Yes, quite frequently, particularly in crowd simulation. Actors within the crowd are programmed with particular behavior types and will interact with each other to form a more lifelike crowd. The interactions are usually fairly simple, but it is a form of AI. I'm not sure if it is still around, but one of the early programs used for this was actually called "Behavior".
Some procedural animation could also be described as a form of AI as well. For example, when a character needs to walk across uneven terrain, it can be possible to setup a physics simulation and have the character alter their movements to maintain balance. This is really also a form of AI combined with physics simulation.
There are probably others as well, but those are the first two that come to mind as relatively common uses.
I don't think it's very common. They use animators, which may have set movements, which they can queue at certain times. Self-interactive AI seems like it would take too much time to program and reprogram.