Saints Row 2 has a slight glitch having to do with reloading. Usually, your nameless protagonist will reload dual SMGs by spinning them in his/her hands and keeping them at his sides. Sometimes holding down the button makes the game act as if you are still firing while you are still in a reloading animation. Meaning it looks like the guy you took out in front of you was killed by some crazy richochet.
Go at a high speed and ram a gas station pump. You'll blast off farther than the Team Rocket trio.
Saints Row the Third has a bug where, on occasion, the D4TH Blossom SMG just fires from its total ammunition without the Boss having to bother with replacing magazines.
Mafia has several. For instance, while the civilian population's driving AI usually works fine, it sometimes fails amusingly, leading to 'drunk drivers' barely managing to stay on the road and eventually crashing into obstacles. Also, try getting out of e.g. a racing car and stealing a car from gangsters. They will in turn get into your abandoned car, pursue you with it, and die horribly as their AI can't cope with a car that fast.
Another incredibly useful exploit: Reload your weapon and immediately perform a sideways roll to have your weapon be instantly-reloaded without having to wait for the reload animation to complete.
And Resident Evil 4. Unfortunately you could only dodge when you're being attacked, and most enemies don't give you enough of a warning to use this bug reliably.
Gears of War final boss General Raam is extremely difficult for two reasons, his handheld minigun and his shield of kryll bats. Mercifully, it is possible to trick him into standing behind the last cement block to the right of the platform where he appears, where he stops moving and does not target you with his gun as long as you don't stick your head up from cover. Getting him into this glitch spot is tricky and the other sources of damage can still get you on insane level, but this trick is enough to bring down an impossible fight to an almost manageable one.
The Mass Effect 2 character import tool has a glitch where a Mass Effect1 character file that completed the Conrad Verner side quest with the Paragon outcome accidentaly triggers both the paragon and renegade flags which the second game always treats as a Renegade outcome, resulting in Conrad gushing how awesome it was when "you put a gun to his face." This never happened of course and only results in Conrad looking even more deranged and delusional, adding to the character and allowing Paragon players to experience a side quest that would have otherwise been absent.
In Mass Effect 3 Conrad apologises for claiming you threatened him if you actually didn't, adding that he was under a lot of stress at the time.
In some scenes in Mass Effect 3 when a character tries to turn their head to face someone when speaking to them, but the character is behind them, rather than the character model turning, the entire head and neck will twist around 180 degrees. Usually this just happens during non-cutscene dialogue, but a conspicuous example is after Priority: Geth Dreadnaught where Gerrel's head will twist around in an otherwise dramatic, high-tension scene.