Personally, I think AI makes games playable for the designer, which helps in testing and being able to judge the fun factor in a game. Really important for a single game maker. How do you test a puzzle game when you are the one that designed it? You can test a platformer, but as you get better, the game will seem easier and you might mess up the starting levels. Even simple AI with some random behavior kind of brings a game to life. Also, as you play your own game, you will keep getting ideas on how to make it better.
The second thing is being able to make enough choices in equipment so you can experiment with different strategies, not really related to AI other than making it even more complicated.

Its just because almost anything is called AI this days...
Even very old games, like one of the first games ever pacman, is considered full of AI nowadays.

    IceBergyn I don't think too many games are using what's considered AI now days, if there even is a definition. We've been doing it for years and years and everyone knows it's just sleight of hand, but it does work in a game to offer more interesting behavior. It's still enough that a game becomes something you can play more than once, where as, a simple puzzle game, once you figure it out, you are done. You can't even test it. I have written puzzle games and you don't have any idea if a puzzle is too hard unless you get some game testers.
    The trouble with game AI is it ends up being used in combat and that's about it, but still, even chess is basically a combat game. There's a case where it definitely feels about the same as playing an opponent, and I'm sure it's not true AI. Anyway, I was just talking about the simple kind we have been using for years. I think even the Sims has millions of lines of code and it's kind of outside a lone developer. We can't get much passed having a little priority list of action with a little randomness thrown in.

      IceBergyn Bro, this if statement just..KNEW WHAT TO DO? Robots, man. You can't get away from them, they're in the code now :-(