Grand Theft Auto: San Andreas would occasionally spawn aircraft that had a flight plan going straight into the ground, assuming the player was at certain parts of the game world (the tops of a rural mountain). The dev team discovered this bug when the game was being tested and decided not to fix it.
This bug has been seen in the middle of a crowded intersection, which destroyed several cars and killed many people. Assuredly, worth the price of admission as the bug was not known of at that time.
There is another bug in this game where, in some 2-player situations, player 2 can decapitate player 1 (with the sword) and player 1 will respawn headless with blood spurting out of their neck.
A cool visual glitch can be triggered while riding the Mountain Bike. Mash the X button while holding the Square button and watch as CJ's limbs stretch, twist, and bend in all sorts of uncanny ways. Do it enough and he'll even start to melt into the ground.
While riding a bicycle, it's possible to climb up inclines at angles just shy of straight vertical by repeatedly mashing the accelerate button.
If you play the PS2 version of the game with a tool like HDLoader, the delay between spawning vehicles drops to almost nothing. This is mostly harmless, as the same amount of vehicles spawn, just sooner; however, it interacts badly with the buggy highway driver AI, which results in VERY BIG pileups if you approach certain intersections in Las Venturas on foot, or occasionally spontaneously on some highways with no provocation whatsoever. A well-placed grenade in this situation can set off a neverending chain of explosions that is continually fed by the rapidly-spawning vehicles adding to the pileup as cars are destroyed.
Several "ghost" vehicles are in the game. These tend to be due to odd spawn conditions within the game itself, the most famous being the Ghost Cars in the hills of the Back-O-Beyond. They spawn at the top of a hill and roll slowly down, heavily damaged and completely driverless. Others include a "ghost hovercraft" at Bayside and another "ghost" car at Mt. Chiliad, even though that one has a driver. They don't do anything particularly useful, other than give you some transportation, but they are definitely creepy.
And on occasion, dangerous if you don't see it coming. Nothing like an empty car slamming into yours just inches from your face...
Using the jetpack and some careful maneuvering, you can get into some rooms and other areas that are normally contained only within cutscenes, as detailed here.
In Grand Theft Auto IV, there is a swingset in the game's version of Brooklyn that is unintentionally buried inside the concrete under it. The physics engine realizes this is a problem, and constantly attempts to dislodge the swingset with brief moments of infinite force. If you drive a car onto the swingset (or climb on it yourself), said infinite force will destroy the vehicle, kill the person... oh, and launch both of them into low Earth orbit. It's a popular spot for YouTube videos.
If you position your character on a ledge just right as the police are moving in to arrest him, a long line of police will jump onto the ledge and fall off like lemmings. Works when you hide next to billboards too. (See example here.)
Call up a friend to go drinking. Walk to the bar, or park just before getting there. Pull out a gun and go to the bar. Now you are stumbling around drunk with a loaded weapon that you can fire. Especially funny with a shotgun or automatic weapon. High probability of shooting yourself in the leg or accidentally blowing away your drinking buddy.
Hell, even DLC isn't immune to this sort of thing. In Grand Theft Auto IV: The Ballad of Gay Tony one of the weapons you can get is an Assault SMG. However, you can't fire it while in a car... unless you exploit a glitch in the PC version that lets you select it, although it will only shoot at 1/5th of its normal speed.
Grand Theft Auto V has a glitch that allows you obtain three vehicles normally only obtainable in the Collector's Edition of the game. This can also be used to bypass Rank requirements in Grand Theft Auto Online.
Another Online glitch involves getting to snowy North Yankton. One does this by starting a new game in the Campaign, then during the mission set there, enter Online mode. Hop in a plane and fly up, and you will eventually get to North Yankton. Explore to your heart's content, but be wary of certain areas, such as an open grave in the graveyard, that might drop you right back into the Pacific Ocean.
In Grand Theft Auto: Vice City, sometimes if there is a body or object next to the open driver's side car door, and you try to get in, Tommy will instead run in a U from the hood to the back tire trying to find the door. Sometimes he will even bump into pedestrians who will then start fighting each other! A riot because the poor guy can't find his car door...
True Crime was loved for the massive amounts of bugs that took place with its random crime missions. Notable examples are when the designated mugger tries to mug the player, a villain trying his best to run through the wall and a villain car being destroyed before the mission begins.
If you drive at full speed while heading directly at wall, the chances are you will drive through it as if it weren't there.
The space trading game Frontier: Elite II featured a 16-bit math overflow bug whereby the player could transit distances of exactly 655.36 light years instantly, using minimal fuel. The "wormhole bug", as it became known, was almost essential for exploring the outer reaches of the in-game galaxy, although sadly it was removed with later patches.
A more useful bug in let you obtain as much money as you want. All you had to do was accept a mission to carry someone to a different system and then try to sell your ship. You'd get the money for the sale of your ship, but the game wouldn't sell the ship because there was someone still on board.
The early versions of Frontier had another useful bug, there was a system in which gemstones had a negative value - they paid you to take them away - and in another nearby system they were illegal, which doubled their black market value. You could make ludicrous amounts of money exploiting this bug.
Elite II also had a bug which allowed laser turrets to be aimed while game time was paused. You could wait until the enemy was close enough, pause the time, take all the time you need to aim, fire your laser and unfreeze time to watch the enemy take a certain hit.
Frontier First Encounters, the third game in the franchise introduced Thargoid Warship which you could obtain by doing certain scripted missions. The creators of the ship also fill your cargo hold to the brim with Alien Artifacts - the most expensive trading good in the game. Well, the bug caused the cargo to be filled well beyond the brim, capping at 65000+ tons of Artifacts in your hold. This was fixed once you saved the game - it would return to 140 something tons. BUT! If you went back to core systems without saving you could sell all 65k tons of Artifacts for ludicrous amount of money, effectively making cash a no-factor in subsequent play. Better yet. After you emptied your hold of Artifacts you could load up anything (water being the obvious choice being the cheapest and most common good available) onto your ship and THEN save your game, which would not revert the cargo space to the original amount, as was the case earlier! Congratulations. You now have a ship that not only sports four best lasers in the game, has the most insane range, but which has a cargo space equivalent of 30+ biggest freighters in the game! Put 1000 Shield Generators on it and you're indestructible. You can now safely ram planets.
Crackdown has an interesting physics glitch made possible by the "Keys to the City" mode. Turn off pedestrian traffic, set your driving skill to four stars, and spawn an Agency SUV. Drive as fast as you can on one of the larger highways with the Keys menu open, then spawn a ramp truck when you reach an upwards slope. If done correctly, the SUV will be launched at an absurdly high speed sideways, usually either slamming into a building or flying a couple miles out into the ocean depending on where you were and how fast you were going. Seeing a tricked-out SUV doing barrel rolls as it flies sideways over a Ferris wheel at Mach 2 can be quite entertaining.
Using Keys to the City, one could create a kind of staircase by constantly spawning ramp trucks if they were quick enough to pull it off. This allowed players to scale tall buildings without having to go through an army of mooks on the way up, or just see how high they could climb into the sky.
One of the few actually useful ones allows you to use Dead Eye - a brief moment of painting targets and shooting them with 100% gunshot accuracy - with Molotov cocktails and dynamite. It functions exactly the same way, just with an invisible crosshair. Can you say homing explosive projectiles?
Horses have a stamina meter that's supposed to drain if a horse sprints at its maximum speed, but if you press the sprint button at a certain speed, the stamina will recover more quickly than it's spent without your horse losing speed, effectively giving it unlimited stamina.
Stagecoach rafting. Stagecoaches have a floating quality which allows you to sail along water. There aren't many places where you can successfully raft, but most of them can take you a long way before you stop. You can even get across to places you haven't unlocked yet. Sometimes, you can even see posses going for a sail in Multiplayer.
Like Dwarf Fortress, the strange interactions of Minecraft's world create a lot these: Swimming up waterfalls? Teleportation via minecarts? Sand-on-torch floodgates? Glitch after glitch has been discovered, explored, and developed by the massive Minecraftian community, before being turned into yet another incredible, important and intriguing tool for future players. They've started fixing them now, much to the dismay of players who can now drown in a small waterfall.
No mob in the game can see you through glass, they all treat glass as a solid object - until they can 'see' you at least once, following which they will be able to detect you through any block.
A (now patched) glitch let you duplicate items by storing an item inside a chest, then closing the chest while still dragging the item, causing a dupe item to drop in front of you.Although the duped item would disappear if the player attempted to use or stack it, it could still be used to craft, making mass production of iron or diamonds a reality.
The booster cart glitch, which allowed minecarts to speed up considerably, had an entire subway system founded on it. Notch, one of the game developers, didn't get rid of them in a timely fashion, but added in a replacement feature (powered rails) that works without any glitches, albeit differently. He then proceeded to remove the glitch boosters in the next patch, along with boat elevators and rapid-ascent water ladders, to the dismay of the community.
In an attempt to make powered minecarts work again, the glitch (albeit weaker, but still useful) was reintroduced. Notch and Jeb just can't win.
If a multiplayer server is experiencing significant lag, you can see flying squids.
Normally sand and gravel blocks will be subject to gravity (the only two blocks in the game that are) and fall down if you remove the block supporting them. However, due to the way the game world is generated, you can end up with floating sand/gravel blocks. If you place a block next to one of these, the physics engine will recalculate the floating blocks which can result in large areas of apparently solid land suddenly caving in and collapsing. If done right, you can use this to make pitfall traps, or just make cool floating structures that shouldn't be possible.
In some of the older versions of the beta (prior to 0.8), using "404" as a world generation seed would create a gravel patch in this manner; upon destroying one of the gravel blocks, the sand and gravel in a rather large area would spontaneously collapse and reveal a giant sinkhole from sea level to near-bedrock. Various players had thus participated in the "404 Challenge", which involved surviving in the sinkhole with (among other limitations) no torches.
While not strictly a glitch, the water physics in Minecraft are very peculiar and players have found all sorts of inventive ways to exploit this to their advantage.
As of 1.7 there's a glitch that allows the player to duplicate any object they can place in a flowerpot, by destroying or moving the block bellow the flower pot. The use of redstone can turn this into dye factories or semi-automatic tree farms.
The liquid physics in Terraria have their own issues, allowing players to create water and lava "generators" that take a small amount of either fluid and duplicate it infinitely.
For a short time (About a Week) of the 1.2.4 update, if you set up minecarts in a particular way and held the break button after getting some automated speed, you could go into hyperspeed. If you used an item during this time, you'd go flying off the minecart and PHASE THROUGH SOLID MATTER.
In Mercenaries 2, a glitch exists where if you lose enough times, particularly in the Bird Delivery Mission, for some reason the bad guys will stop shooting at the player. This glitch lasts until one quits the game. During this time, one can beat the side missions that are normally impossible to complete because of the attacks.
The first Mercenaries game also had a rather amusing glitch known to the community as "Spinning Artillery". If you shot a soldier driving the open-topped ZSU-57-2 and killed him, the vehicle would begin to spin in a slow circle until boarded or destroyed.
In the game Bone Town, one is able to have normal sex with the special characters in the Fantasy Mansion. Just need to stand far away from said woman, and slowly move in while hitting the Enter Key until the scene occurs.
Brock, the final boss in Overtime Mode in Dead Rising, is usually extremely difficult to fight and rather unfairly, the game takes away any weapons you had before starting the fight. However, there is a trick to get around this. One of the mixed drinks you can make, called Spitfire, allows you to turn your spit into a projectile of sorts for a few minutes. It's not that useful in any other circumstance, but if you make one before giving the last queen to Isabela, take it with you, drink it before entering the Jeep and defeat the tank as quickly as possible, you will still have the Spitfire effect as you start the fight with him. This allows you to run away a short distance, face Brock and spit at him repeatedly. He will block every attack, but he will slowly take damage and will eventually die. Call it unfair, but it's not like he plays fair either.
Saints Row: The Third has a glitch with special weapons like the minigun or shock hammer in Mayhem activities. Basically, you're restricted to certain specific weapons for the activity, and cannot pick up or select alternate ones. However, gang specialists and brutes, who have unique weapons, still arrive to attack you if you end up getting a ton of gang notoriety while causing mayhem. You can still hold the reload button to pick up their weapons once you kill them, at which point your character just holds them in their hand and acts as though the weapon doesn't exist, leading to such sights as holding a minigun one-handed or mashing it together with an RPG.
In Batman: Arkham City, if you stand at the edge of building and start throwing Ice Grenades, Batman will start to rise vertically with every throw. Sounds interesting on its own but if you get high enough you can escape the normally impossible walls of Arkham City and explore the rest of Gotham, which despite only being seen in the distance, is breathtakingly detailed. The buildings don't have collision so you cannot grapple or stand on any of the buildings; you only get one glide to view the city of Gotham, but most view it as worth it to do it at least once. Here is a link.
The final mission of Saints Row 2, which can easily be That One Level if you're not good with the game's helicopter controls, can be somewhat eased if, immediately after getting into the helicopter provided, you get back out again and run around for a little bit, resolutely refusing to engage with the attack helicopter that is sent to shoot you down. After a couple of minutes, the enemy helicopter will seemingly get bored and fly away, and oftentimes it will not be replaced with subsequent iterations as it would be if you shot it down. This makes that part of the mission much easier.
The zombie survival gameThe Dead Linger is still in its Alpha stage, so of course it has several bugs, some of which work in favor for the player. Besides the possibility to run endlessly without your stamina depleting by just holding Tab after you started running, there's also the famous "flying" glitch. By taking any movable object that's big enough to stand on it (mattresses are the preferred choice), standing on it, looking down and grabbing it with the middle mouse button, it starts to ascend, with you on it. You can even steer it and fly wherever you want. This way, you can not only evade the zombies on the ground, but it also helps you with your building projects.