At the very start of the first Red Faction, you're supposed to watch a fellow miner get into an argument with a guard and then get killed, sparking a riot and subsequently the rebellion. However, if you go past the guard and miner grappling with each other you'll trigger the script where the guards start shooting at you prematurely. Normally, this would have been a bad thing since you can't fight back until you grab the baton from the soon-to-be-dead guard, but if you stand behind the grappling duo the guards will shoot the grappling guard, killing him - and the miner will keep wrestling with empty air before falling to the ground and dying for no particular reason.
Throwing a remote mine on Exposition Fairy characters in the first Red Faction game. Their animations would still show them talking civilly with you, but all of the dialogue will be replaced with them screaming. After they're done, they'll go right into flailing their arms and acting frantic. Funny!
How does Alias force Sopot to comply with him when they meet face-to-face halfway through Red Faction 2? By slapping him across the face in what should be a serious scene, that comes off as hilarious. Like how Alias swings a grenade launcher at them but only has a light slapping sound, or wears the guy's hat almost immediately afterwards.
Sgt. Winters from Armageddon has this comedic gem in the lava level:
Sgt. Winters: You ever notice how when bad things happen - I mean the absolute WORST things imaginable. Horrible stuff - there's always a Mason around? Now I'm talking about shit you couldn't even dream of happening... y'know, it never fails!
When Darious punches out the Jerk Ass Colonel, which doubles as a CMOA:
CO: Don't think this changes things. I'm still bringing you in.
Mason: With all due respect, sir- *punches the CO* You're an idiot.
Sgt. Winters: Damn, Mason, you just punched out my CO. Now what am I going to do with you?
Mason: Well, you sure as hell can't detain me.
Sgt. Winters: No, but I can thank you.
Pretty much any conversation between Darius and S.A.M. whenever something bad happens and he asks her for a solution: