Left 4 Dead has a few bugs with destructible environments, especially on Versus Mode. One bug in particular that helps the Survivors is that some terrain and doors are marked 'destructible' so that Enemy Tanks can smash straight through them in order to chase the Survivors through the map. One of these doors is positioned so that once you have gone through a long and painful section of the map, you can flip a switch to open the door to let any lagging or injured survivors into the building without having to run that section of the map. However, because it is marked 'destructible', with enough firepower you can blow the door open and skip that area entirely. This is good for the Survivors, but in Versus mode, bad for the Infected, because it lessens the amount of time you have to eat the Survivors.
Fixed in a recent patch along with many other memorable glitches. On the upside, in Versus the Infected got a status bar!
This exploit came back when No Mercy was ported to Left 4 Dead 2, but made tons easier since the said door in question could instantly break from any melee weapon used on it. It took valve at least three to five patches to finally plug the exploit, which Valve wrote in the release notes regarding the issue to say "Fixed the fix of the fix of the fix of the door exploit in No Mercy"
While the door was fixed, it can still be broken by shooting it with a Grenade Launcher. This bug is not a problem in VS mode since the weapon does not spawn until at least after the event and VS mode does not let players carry weapons and items from the previous map (everyone starts off fresh).
Most of the levels have locations that the infected can't reach, even though they physically can climb up (such as the famous Jesus Rock trick in the finale of Death Toll) or being in certain spots in the finale somehow causes the Tank to glitch out and just suicide almost instantly.
There was also a brief bug in "No Mercy" where, if a player threw an item at another player in the elevator, they would plummet through the floor to the bottom of the elevator shaft. Another bug which had a significant effect on gameplay was that player-controlled Boomers could use the suicide command to explode whenever they wanted, meaning that survivors could not push them away without being sprayed.
The bot AI also has its shining moments of idiocy: For example, try hanging on a balcony that's just out of the bots' reach and watch as they heroically leap over the edge to their deaths. Sure, you'll have to restart the map, but it's worth it just to see it happen.
The TAAAAAAAAAAANK Mutation in Left 4 Dead 2 was a VS mode in which all the Infected players spawn Tanks, all the time. The bug appeared when playing Dead Center. At some points in the first map, there aren't enough places for a Tank to spawn both out of sight of the Survivors and close enough to actually attack them. This lead to Tanks spawning in places outside the building, in mid air, 30 stories up, and falling to their instant deaths.
In a related fashion, for a long time, after the elevator in the first map of Dead Center a tank could spawn with about a 1 in 4 chance of spawning *inside the fire*. While having a giant immolated tank banging on the doors could be intimidating, it wasn't very effective.
Silent Hill has a bug where using the bottle of aglaophotis on one of the Stalker Larvae at the Lake Side Amusement Park skips the confrontation with Cybil and goes straight to the (graphically glitched but otherwise unimpaired) cutscene where the parasite is removed. Its handiness in aiding attempts at ten-star ranks and speed runs has made it well-known amongst fans.
In the second game, there's a mini-glitch during James's battle with Eddie, where he seems unable to move or attack, allowing James to easily destroy him.
The best is perhaps the glitch in Silent Hill 4's Building World revisit that lets you bypass bringing Eileen through the Door of Time like you normally have to, which means not only bypassing the script that spawns monsters in the area but also bypassing all the monsters you have to save her from before then.
In the remake of Resident Evil, you can perform a grenade launcher glitch that allows you to get a infinite number of grenades. Two types of ammo and an item box is needed.
This trick does not work in the PAL version.
In that same game, thanks to the way the flame mechanics were coded, it was possible to burn multiple zombies with one dose of kerosene as long as their corpses were touching. By luring and killing zombies so they fall onto one another, it is actually possible to kill every zombie in the game and only ever deal with the two unavoidable crimson heads that appear in the game.
Resident Evil 5 had a glitch where you could load guns using the inventory... even if they were the gun you had out. In multiplayer, this allowed skilled players to reload near instantly, circumventing the weakness of many weapons and making chaining combos together a lot easier.
Resident Evil 3: Nemesis has the "corner bug" when fighting the eponymous Nemesis in the police station. If you lured Nemesis into a small office in the meeting room (next to the evidence room) and backed into the corner next to the book case then Nemesis would get stuck on the book case while trying to run at the player, keeping him just out of range to attack (unless the player is standing with the knife readied to attack and even then he'll only attack on his initial charge) but allowing the player to attack him without getting hurt, even with their knife. He does eventually get unstuck but he can be lured out and back into the small office and this bug can be repeated until he's dead. This is the only viable way to beat Nemesis inside the police station without using a lot of ammo or healing items.
There's a similar bug in the three-way intersection leading to the cable car in downtown where Nemesis can get stuck on a corner; unfortunately, this is only in the Japanese version. In all English versions this corner bug has been fixed.
Stalker: Shadow of Chernobyl, a notoriously buggy game, had some good glitches:
The game world is littered with anomalies that cause damage to the player. The player can get artifacts that increase damage resistance. Once you have the rare artifacts necessary to bring damage resistance over 100%... the once-hurtful anomalies not only heal you, but repair your armour. With no way to repair quickly-degrading objects in the vanilla game... hell yeah.
At some point in development, the devs decided to remove vehicles from the game. Installing mods can restore the driving feature though. Anomalies that usually pick up the player and turn them into mush affect vehicles differently; they toss the cars through the air, sometimes at great heights and distances, over buildings etc.
It's also possible to drive the vehicles without the mod through careful use of clipping. Hilarious. Hell. Breaks. Loose.
One of the side-effects of removing vehicles is that they never properly coded what happens if a player comes across one and tries to use the ridiculously-powerful knife on them. As such, the vehicles that are still in the game can be destroyed by stabbing them one time.
In Call of Pripyat, a character named Crab is scripted to stay laying in a bed on the Skadovsk. Sometimes when you load a game where you saved on the Sakdovsk, Crab can be found out of bed. He then starts living up to his name. It's as hysterical as it is terrifying.
This game has, however, one really good bug. After beating the game, you get access to the "Impossible" difficulty. It is a harder version of "Hard" and it would be terribly difficult... if you couldn't keep your suit from the previous game using a glitch.
Dead Island has the weapon duplication glitch, which makes a copy of your currently-equipped weapon. This allows you to use your most powerful weapon alone, as well as throw them away when they break, skipping maintenance benches completely. Not only that, you can also earn essentially infinite money by selling a pile of duped weapons.
If the glitch occurs with a firearm, a large amount of ammo will appear in the gun's current ammo supply, potentially well over ten million. While this prevents you from picking up ammunition for the weapon in question, it's more than enough ammo to kill every enemy you'll encounter in the game, and then some.
In both Amnesia and Amnesia 2: A Machine for Pigs the player can finesse to on top of the nemesis monster, rendering it completely unable to reach the player. Spoiler Warning demonstrated this in specials for both games, and found it hilarious enough to declare it a win-state and quit at that point.