Alone in the Dark (1992): The first hallway you enter, there is a large chasm in the floor, and a door to your left, and to your right. If you take the door to your right, a Zombie will follow you in. If you take the door to your left and block the door, you'll eventually arrive at the other side of the chasm and you can see the zombie walking into the blocked door.
Your pawns in Dragon's Dogma can really make fighting cockatrices and Death suck. Both of those enemies can kill all of your pawns in an instant and pawns aren't programmed to dodge the attacks that do that.
If you're fighting an enemy who can only be killed with projectiles but you don't have any, your projectile-wielding pawns will usually spend the entire fight running in random directions and yelling that someone needs to use a projectile.
Daimon has an attack that sucks everyone in and kills them. Pawn reactions include running into the attack on purpose, walking away from the attack so slowly that they quickly get pulled in, standing still, and attacking the suction with their shield.
Pawns don't like running from enemies but they don't like fighting 'em or healing themselves either and they don't follow you closely when enemies are around.
The Legend of Zelda: The Wind Waker has notoriously horrible enemy AI and literally nonexistent pathfinding. If an enemy spots Link, it will try to chase him down on a completely straight path, even if said path leads into a cliff face which Link is on top of. Enemies make no attempt to avoid obstacles such as unclimbable slopes. The enemy AI is often cited as an example of the game's lax difficulty. They'll also hit and kill enemies that happen to be in their way. Your enemies. Moblins will clobber each other trying to hit you, Darknuts will mow down foes standing between you and them, etc. It's actually a viable(and hilarious) strategy to use stronger foes to wipe out the other enemies for you, especially if there are a lot of them, or there are several strong monsters.
In the spin-off Hyrule Warriors your allies' AI is practically non-existent as they stand around and do nothing but watch the player character running around all over the battle field and doing everything on their own. The stupidity is most noticeable when one Cannon Fodder minion is surrounded by a good ten of your allies and it takes several seconds before even one of them decides to swing its weapon in the general vicinity of the enemy. Fortunately, the enemy AI is just as stupid.