Invoked in Sam & Max: Bright Side of the Moon. A quartet of sentient obsolete computers are attempting to devise the most advanced AI ever, and you have to play Tic-Tac-Toe against one of them. The AI is just about as sharp as advertised, except for one problem: it actively plays to lose rather than win, so convincing the computers that their AI really is invincible by losing to it takes some doing.
Enemies in Ratchet & Clank: Up Your Arsenal can be briefly summarized as "utterly imbecilic". They will run over flamethrowers, don't seem to notice that they are attempting to shoot through their own allies, and generally have issues with the whole "not acting like a moron" thing.
Not all enemies are entirely stupid, however. Some have at least some grains of sense, like hiding behind corners and leaning out to shoot you. And some, like Robo-Troopers, seem to do smart-ish things like having their front ranks kneel and fire while the second rank stands and fires.
Regulus in Bomberman 64, when helping you against Sirius, is nothing short of a dumbass. He'll typically do nothing but wander around the area and occasionally drop a few bombs. Sirius himself isn't all that bright, either, since the way he behaves with bombs will make him blow himself up if a bomb he's already set down is detonated by something else. This makes it very possible that he'll end up dealing the final blow to himself.
The Red Eyes in Star Fox Adventures. Unlike the other enemies in the game that attack when you enter their line of sight, they are programmed to move in a set pattern and will only attack you if you enter it, even if you are right of front of them. This is makes sense in context, because until you get the super ground quake, you can't hurt them.
The combat system in Quest for Glory IV is changed to include a strategy mode which, rather than the player directly controlling the Hero's actions, instead allows the computer to do so, based on the Hero's current skill levels and settings defined by the player. The AI controlling him, however, is less than useful, and no matter what settings you use generally ends up as Attack! Attack! Attack!.