The Mad Hammerer, one of the creator's favorite bugs. A Hammerer carries out death sentences by striking the prisoner with a hammer. If unable to wield a hammer (due to both arms being broken, for example), he would instead bite the subject to death and walk around with the man's bitten-off limbs in his mouth forever, until they start to rot.
Toady's other favorite bug involved a farmer walking to a furniture stockpile, picking up a bed, then walking to a farm plot and planting the bed as if it were a seed. This was patched before release.
Other bugs that tend to be mentioned nostalgically: infinite magma floods, serial killer elephants, the dwarves' utter indifference to being on fire. Note that all of these were part of the legendary Boatmurdered.
The "on fire" bug would particularly dangerous/hilarious when combined with a fortress's highly-boilable booze stockpile, which dwarves would regularly visit for a drink.
You could also site your fortress overlapping with a human town... then proceed to undermine their buildings, causing them to collapse, and raid the rubble for fortress materials. Where this enters Good Bad Bug territory is the fact that the humans don't care, and you could massacre their population, destroy their city, and steal the shattered remnants of their belongings without their losing the "Friendly" status.
The absurdly overpowered throwing. A character can mangle a body part and brutalize enemies' internal organs with a pebble, a coin, or even vomit. Throwing was nerfed in 2011, but you could now pinch people's heads off.
They can also bash enemies to death with their own pants, or fell someone with a well-thrown sock.
"Tamed" animals that have killed dwarves in past...aren't. They spend their time gleefully slaughtering the hairy ones, who still believe them to be tamed. The main way to stop this is to order the critter butchered as soon as you tame it, which gets you a lot of raw materials if it's something like a dragon or titan.
There were also (sadly removed) bugs involving individuals ordering someone to hurt them - fortress mayors sentencing themselves to be beaten when their own mandates failed, and assorted folk in Adventure Mode requesting their own assassinations.
The carp. Sweet Armok, the carp... A bug in the skill system meant anyone could buff up their stats by swimming. Seeing as they do that all the time, the carp became invincible monsters.
While the carp have stepped down, giant sponges have taken up their mantle. Since the engine can't handle an unmoving animal properly and has some issues with determining the death of creatures without body parts or blood, they'll push your dwarves to death and are immune to normal weaponry. Even more ridiculously, examination of their raws indicates that they can be ridden on as war beasts, though nobody has reported any invaders using spongy mounts. The hilarious nature of the threat, along with its nigh-invulnerability, have made them nearly as famous as the carp of old.
Without a nervous system, the only thing they can feel is ANGER.
Similarly, constructions of any type are completely invulnerable. Not only does this allow you to hold magma back with ice walls and wait out a forest fire inside a wooden building, it also means that a rampaging hellbeast that can smash whatever doors, floodgates, and bridges you put in its way will be stopped dead by a wall made of glass.
The existence of Planepacked, the best artifact ever: a giant monolith decorated in fine detail with the entire history of the world, including several depictions of itself! It's probably safe to say that the bugs are half the fun of Dwarf Fortress.
In the initial builds of the 2010 version, it was possible for animals and dwarfs to melt in the rain. What happened was that Dwarfs got covered in water and high temperatures will heat this water. This then caused the dwarf's fat (whose melting temperature was much lower than it should be) to melt off. Naturally, this being Dwarf Fortress, this was soon put to good use.
A typical fort in the 31.10 version was less than 200 Z-levels tall. The ultimate metal, adamantine, is only found deep underground. An erratic bug in world generation resulted in a location having a 2200+ Z-level tower of adamantine shooting into the sky. Forum Thread
Nothing exists off the edge of the map. You can't dig out the edge squares, but you can carve them into fortifications and drain a river off the map with them.
Certain powerful enemies are rampant building destroyers, taking out floor hatches, floodgates, workshops, and anything else they can get their appendages on. If a door they'd like to wreck is jammed open, they will politely wait for it to close before doing anything at all.
The danger room, where military dwarves are stuck in a room with training spears used in an upright spear trap hooked to a repeater. The spears are unable to actually hurt the armored dwarves but quickly give massive boosts to blocking and dodging as well as lesser boosts to weapons and armor skills.
A few materials, notably lignite and graphite, have an ignition point but no melting point. Thanks to this and a quirk in the way items in containers are tracked, if you put some in a bin and light it on fire, it never goes out. You can drain an entire ocean into a bin full of burning lignite.
If pieces of wall/floor fall into liquid due to a cave in, liquid displacement is simulated by vertically teleporting the displaced liquid to the nearest empty space. Players have taken advantage of this to create the "magma piston": a hundred level (or more) high stone column carved out of the earth and made to fall into a pool of magma, causing the magma to teleport up a hundred levels.
This, along with bugs like the ability to store an infinite amount of stone on one square if you mark it as a dump site, is such a savings in time, energy, and not-killing-your-frame-rate that some players don't even consider it an exploit.
Things get really hilarious if there are duplicate raw entries after modding. You can end up with mysterious, typeless "meat", the extinction of the turtle, and even a fortress where instead of dwarves, you start out with extremely dwarfy elves... or, perhaps, ducks.
Heat usually doesn't kill you by burning, it does it by melting your fat. This has lead to a bug where if all the fat is melted off of a character without them dying (surprisingly actually easier done than it sounds) they become effectively immune to fire long term.
Vampires don't need any sleep, food or water, but they count as members of a fortress still. It only took a short amount of time for players to figure out that if you wall vampires into the walls of your fortress they make it effectively immortal, as long as they doesn't go insane.
Most Harvest Moon games tend to have at least two or three bugs each - though this has become rarer since Tree of Tranquility. These are usually among the annoying kind, but a few fit in this category. Among them:
HM's Day/Night system: Time seems to pass normally in an accelerated cycle, except for one thing - night will never end until you go to bed. This means that you can clear your entire property, till and plant seeds on every available square, and water each and every one of them...in one night. The only downside is that some tasks can't be done after a certain time of day (most importantly, the shipping bin resets in the morning, so anything you throw in after the shipper won't count until then) - but for everything else you've got all the time in the world!
HM's Love glitch: The game's eligible brides will like you more when you talk to them every day, but talking to them more than once in a day won't do anything... in theory. Actually, if you walk out of her house, then back in, it counts as a new day. Pretty much mandatory for getting the best ending, which requires you to have a wife and a kid... within three years.
HM 64's Horse Betting glitch: If you place your bets with the Mayor's wife, then exit instead of confirming, the bets will go through without costing you money.
HM 64's Dog Glitch: You can raise Karen's Heart Level to red in a single day by continuously showing her your dog.
HM DS's 1 Billion Gold glitch: Hiring the Fishing Sprites during Winter, then shipping junk items (items that ship for 1G each) during a day when they're working for you will set your money level to 1 Billion. There's a chance doing this will invoke a Game-Breaking Bug that will corrupt your save file, make this option a Death or Glory Bug.
Friends Of Mineral Town: When stumbling upon an outdoor Rival Heart Scene, the clock will not restart until you leave that particular area. Stumbling upon such a scene with your fishing pole and basket in tow is an excellent opportunity to load up on lucrative fish and other items. Also, you don't lose stamina during Festivals, so you can power up your tools to full experience (except for the watering can, which can't be used while empty). Both glitches were removed in More Friends.
Back To Nature: On your first day on the farm, where Mayor Thomas will take you on a tour of town, before exiting your house, you can keep swinging your tools (except for the watering can) to gain full experience levels, since the game will lock your stamina level at 1 so you can go through with the required cut scene. Works with any day where you'll experience a cut scene as soon as you open the door, but this is the first one and most easily predicted.
A Wonderful Life: Cook with Ruby Spice as the only ingredient, and it will create a duplicate Ruby Spice, which can be sold for a tidy sum. Sadly, they fixed this glitch in the Distaff Counterpart and the special edition.
HM: DS lets you keep on getting friendship points by showing your pet to someone, with no limit. It is a great way to get early access to Leia the Mermaid.
SimCity 2000 had a bug involving the use of a joke cheat code. In the first SimCity game, typing "FUND" gave you some money, but Sim City 2000 instead offers you a loan at 25% interest (very, very bad idea). However, the game also dynamically adjusts what interest rate you get on regular loans by examining your current loans. Get a few of these joke loans, and the dynamic interest overflows and goes negative. A loan with negative interest? It means you get paid every year for having debts!
Also, the SNES version of the game had a bug involving a careful use of a pause button and the tax screen allowed to drop below zero, which instantly pushed it to the maximum value (then capped at $999999). An easy way to beat any scenario.
Likewise, holding the pause button at the beginning of the Boston scenario allows you to demolish the nuclear reactors before they go critical.
Also, in the original, a player could construct their entire transportation grid out of railroads where regular roads should go. It cost twice as much to set up, but completely eliminated any traffic problems and cut your pollution by an enormous amount.
The Sims 2 has a great bug where the aspiration reward that temporarily boosts toddlers' intelligence got "stuck" once in a while and left the player with a supersmart kid that learned skills at triple the speed. It was fixed in a recent expansion pack.
And broken and fixed and broken... depending on your expansion pack setup, it either is rare/fixed, happens fairly often, or happens every time you use the item.
there was also the potty-training glitch where if you cancelled the action at the right time the toddler would be instantly potty trained. That was fixed at some point too.
You can also, with moveobjects activated, move a Sim somewhere, rotate the camera, and then start making (non-intelligent and temporary) clones of that Sim. Sometimes called the Door-Clone Glitch, since it was named after misusing the door feature in Build Mode. Same cloning process can be instigated by shift-clicking a Sim somewhere when in Buy Mode.
The Nannies were quite glitchy in the sims...they would do shit like light the house on fire, feed babies that were full, ignore the babies, stick around the house indefinitely, etc.
You can make a floating house, and do it without console commands. Place a bunch of pillars down, and then build your house on top of them. You can then delete the pillars, and the house will remain standing. You've wasted a floor of your house, but you can always use that space for one giant swimming pool.
The Sims Medieval had a minor but fairly helpful one just after the release of the expansion. One quest makes you create a food item called Boiled Goo, but if your kingdom wasn't involved in the War a Sim could actually make it any time without the ingredient from the quest. Since it gave a small positive buff it could be an alternative to eating Gruel, which gave a negative one. This has been fixed; Boiled Goo can now only be made in the quest.
The Norn genomes in the release version of Creatures 2 had a flaw in their simulated neurochemistry, so that when a Norn walked into a wall, instead of getting the signal to turn round and walk away, they would often continue to walk into the same wall over and over. This habit became known as 'Wallbonking' and is considered a classic Norn trait among the fandom, even though a fixed genome and later games (mostly) eradicated the behaviour.
This was far from the only problem in the Creatures 2 genome — the Artificial Stupidity was so rampant, it was dubbed "One Hour Stupidity Syndrome." While many programmers released fixes for this, which targeted various aspects of the genome, the original genome is still quite funny, in a schadenfreude kind of way. To clarify, after one hour, the bugged genome would ensure that your Norn would become incredibly stupid, to the point of total paralysis.
The "flying lemon" bug in the first Creatures is fondly remembered by fans.
Other flying objects too, like the coconut crab COB.
A glitch in Spore lets you abuse how the game sets the limits for creature widths to make asymmetrical creatures, with different hands on each sides, or different limbs on each sides. Eventually this was made easier by making it a legitimate game feature.
Also, limbs (but not hands or feet) turn invisible if the starting joint isn't connected to the torso. Somebody made a whole range of Rayman-based creatures this way! This glitch is also very commonly used to make creatures that perpetually hover above the ground (using invisible legs).
Monster Rancher Advance 2 has a Good Bad Bug... that unfortunately comes with a side-order of Laser-Guided Karma. Essentially: At the start of the week, before doing anything else, save your game. Turn it off and on again quickly. If done correctly, your monster will lose Fatigue and Stress points, meaning that, if done repeatedly, they will never tire. The universe's retrobution for cheating to train your monster? If done repeatedly, this trick will actually kill the saving on your actual game, due to its origins as a memory-clearing glitch.
Animal Crossing: City Folk has an oversight in the programming which makes it possible for the player to completely bypass the "normal" methods for getting nearly anything. When you go to someone else's town via wifi and then leave, as you disconnect and Copper wishes you a good day, the player can press the Home button to reset the game. Wifi normally does not let the player use the Home button at all. This allows for cloning items, including money. By having the host save the game, the guest can drop the item in the host's town and then use the oversight to reset the game BEFORE you return to your town, meaning the save when you return will not happen. When you start the game back up, you will have the item in your inventory, and your host will have a copy of that same item. Thus, it's possible for two people teaming up to get as many of a given item as they wish or as much money as they wish, and in this way completely bypass the normal methods of earning money or certain items.
NASCAR Racing 2003 Season: Unrealistic car setups worked well with the original retail version on the faster tracks, to the point that the cars handled more like Indy cars and were somewhere between stock cars and Indy cars in terms of speed.
The original Transport Tycoon keeps cash on hand as a 32-bit signed integer, limiting your money to +/- 2.1 billion GBP (all other currencies are multiples of this base amount; USD = GBP x 2, JPY = GBP * 100 etc). It's possible to build a tunnel extending from one end of the map to the other, which would make the cost overflow. Shift-click to get a cost estimate, keep searching until you see something with a cost in the negatives, then build. Instant jackpot of 2.1 billion pounds. Did I mention this can be done shortly after the game starts? This was fixed in Transport Tycoon Deluxe.
In a similar vein, cash-on-hand can also overflow, suddenly shifting from 2 billion on hand to 2 billion in debt. The AI companies are not smart enough to begin wasting money once it approaches this number.
In X3: Terran Conflict, the ATF Skirnir missile frigate is a Game Breaker even by the standards of its own class, due to an extra zero in the damage values for its anti-capital weapon the Shadow missile. As a result, it puts out 650 megajoules of damage per warhead on an eight-warhead missile. In an unmodded game, the toughest ship has only 12 gigajoules of shielding. Do the math. Egosoft never bothered to fix this in Terran Conflict since you have to board and capture the Skirnir to use it, but what with the full-scale Argon-Terran war in the expansion pack Albion Prelude, the bug was fixed so that Argon players wouldn't get their heads blown off the second a Skirnir showed up.
In ARMA II, an amusing bug can cause tanks (and presumably other armoured vehicles) to fly. By going to the Armory and selecting Utes as the map, the player should be dropped near an airfield. Driving over the boulders just south of the airstrip's centre will cause the game to freak out and launch your vehicle into the air at high speed. As an added bonus, your choice of tank will be completely unharmed when it lands turret-first at 200 kilometres an hour!