I pissed my pants playing Doom 3

Basically, any demon hit by any other type of demon or any zombie hit by anything else would attack its attacker. You had to use this tactic to make it through the secret level in Episode 2, and sometimes, rarely, using this would cause the Baron and the Cacodemon to kill the Spiderdemon at the very end.

I remember that much, but I seem to remember that those two demon types would always go after each other, without any prompting.

Could be faulty recall on my part, though.