In Quake II and III not only are enemies just as susceptable to environmental hazards as the player, but they can and will engage in fights to the death amongst themselves. In Quake III that was expected to happen, since there was only a multi-player game and all the NPCs where bots. But in Quake II singleplayer you will sometimes turn a corner to see a Gladiator bullying a puny Light Gaurd to death or Enforcers shooting down pesky Flyers, who evidently annoy everyone including their fellow Strogg. Not to mention the quickly moving Mutant, which attacks everybody without prerogative including other Mutants. Basically if a Strogg meets another Strogg of different class, they might just duke it out, with guns, and explosives.

Strogg of similar types usually get along, but can be provoked against each other. The AI in Quake II wasnt too advanced, but it was advanced enough that if you took a shot at one, hit or no hit, they would probably come by to investigate. If you could enact a scenario in which you took a shot at a Strogg, and he turned or came to investigate and found another Strogg, sometimes they would fight. Sometimes the unit would just look around for a bit then go back to it's patrol route or gaurd position. The Strogg occasionally seem to get frustrated and fight amongst themselves when a group gives chase and you manage to evade.

As a side note: The Strogg units seem to be a bit more tolerant of the Medic unit, for logical reasons. Some of which may be that the Medic has a Gladiator type lower chassis, a Berserker cutting arm, a mounted Tank HyperBlaster, and 300 Health.

By The Way: What is a grown man doing playing "Chip 'n Dale: Rescue Rangers"?

iandunn says the enemies also fought in Doom, another iD game.
Pulsedriven says in Prince of Persia the enemies could be hurt by obstacles
arrogantsob says obstacles also do damage to enemies in Streets of Rage
amib says there was friendly fire in Marathon and that shell projectiles in the Super Mario games where not discerning between Italian Plumbers and Color Coded Koopas, not to mention that in Mario 2 enemies could be picked up and thrown as weapons
amib says Throwing enemies or beating enemies with other enemies is REALLY common. Gunstar Heroes, Double Dragon, Final Fight, almost every side-scrolling brawler...