Absolute dumbest enemy I've seen in a game are the Light Guards in Quake 2.
In their attempt to get away from the enemy AI that knows exactly where you are as soon as they're activated (while stupid, it's really effective), id programmed the enemies in Quake 2 to go toward your last known location (i.e. where you last shot your weapon). Unfortunately, the AI had no path finding, so it wasn't unusual to enter into a room, look over to your left and see a Light Guard running into a wall.
Mind you, it wasn't unusual to see a Doom enemy caught on a wall in a vain attempt to run *toward* you, the Quake 2 guards would just be running into the middle of a flat wall at some random direction that was in no way at all facing in your direction. You could just calmly walk up behind them and put a bullet in the back of their head at your leisure.