Both Myth I and Myth II have an excellent bug: menu pops up when pressing Esc, pausing the game. What the game doesn't do is to prevent you from giving orders when menu is active, thus this can act as an active, if not tedious, pause.
StarCraft has quite a few bugs which have been incorporated into the metagame, the most prominent being the mutalisk stack, a pathfinding bug which causes air units to occupy the same space, making focus-firing impossible. Not surprisingly, the developers are breaking the engine to incorporate stacking into the sequel.
Of course, who can forget that both the Terran Valkyrie and Protoss Corsair from the expansion were specifically designed to deal with those stacking air units.
By using fan made map editors, a bug similar to this allowed for an entire new game type known as Stack Defense (Stack D for short) which consisted of players using "lights out" commands to "turn off the lights"—activating fog of war even where the player controls units. Usually this would be considered a disadvantage, but it happens that the game doesn't particularly care if you warp in 20 Photon Cannons on the same spot as long as Fog of War is covering that spot when it happens. Then turn the "lights" back on and you have either several structures on the same spot (so that you can't tell there are more than one until they start shooting at things) or overlapping structures forming a wall.
There is also the "Fastest Possible Map" craze, which takes this to the standard battles, where the entire concept of searching for new bases is rendered obsolete; you're given 10 mineral beds with 50,000 minerals one square away from your base, which is contrary to the normal minimum of three you get everywhere else, as well as the 10 vespene geysers two spaces away, each with 50,000 gas. There exist dozens of these maps now, and only two other Top vs. Bottom maps are ever played any noticeable amount.
Lights on/off stacking has some bugs of its own. The maps have a maximum unit limit onscreen at one time, maximum number of objects, and buildings. Meaning if you stack fifty cannons in one spot, you'll end up with only 5 or 6 of them firing at one time, and depending on the wave of enemies the map spawns, you can have none of them firing at all!
This overlapping movement proved so useful in simply getting a huge aerial army from point A to murder target B, that when Blizzard's next RTS, WarCraft III, had some issues with large groups of flying units, they patched in a modified version of the bug - one that turns off the moment they reach their destination, shooting the units out at high speed into focus-firable formation.
Honestly, making custom maps for StarCraft requires using many Good Bad Bugs and a substantial amount of Dummied Out content, in addition to some odd (non-glitch) quirks in the game. The most common example is Hyper Triggers, which cause triggers in the map to execute much faster (almost once a frame, as opposed to once every two seconds); this requires adding four triggers to the map that always execute and do nothing but repeatedly call the Wait action, which normally pauses a trigger's execution. (On the other hand, running hyper triggers will cause chaotic effects if the Wait action is used normally; this is one of the main reasons for Death Count timers.) Extended Unit Deaths are another example, where a condition that checks how many times a player has lost a certain type of unit is used to read other portions of the game's memory, such as how many HP a unit has (which, oddly, the game does not normally allow). Computer-controlled Medics will try to heal injured allies anywhere on the map, causing the Medic to move; this can be used to detect a unit being injured. AI Dark Archons will move to cast Feedback, which drains a caster's energy and damages it based on the amount drained, at infinite range if it will kill a non-hero, which can be used to detect either damage or spellcasting. The list, as they say, goes on.
In Starcraft II's single-player campaign, once you max out Zerg and Protoss research, you can redo previously-completed missions, and the game will deposit some free research points in the research console (without telling you). If you check the console, you get credit for them. Why is this good when you've already completed the research? Extra research points are converted into credits, and even if you found every normal research point in the game and did every mission to collect every single credit, there isn't enough money to max out all the armory upgrades. On the other hand, by utilizing the bug after every mission, you will always have super-units except for the mission you first get them.
Stronghold Crusader has a glitch that, upon pausing the game, suspending the activity of a building, resuming it and then unpausing the game, marks the building as unoccupied without firing the current worker, making another worker take up the job while the old one kept working.A player could repeat this glitch at their heart's content with interesting results, such as feeding a 100+ people fortress off a single apple patch with a dozen farmers, immensely speed up transportation of materials, or fill up the armory in one single production cycle.
Command & ConquerTiberian Dawn and Red Alert, the first two entries in the series, both have a bug where a grenadier can throw his grenades across an entire screen if you change the target halfway through him throwing it. Particularly pronounced in the DOS versions. If you had radar, the grenadier could fling his explosive payload across the map.
You can use game editors to replace the grenadier's payload with something more entertaining, like a nuclear warhead, then making a game out of using this bug. "Can I time it right so the grenadier flings the grenade far enough away to not kill himself and everything I hold dear?" The answer is usually no. It's a tough bug to use.
Tiberian Sun makes long-range grenades intentional, and documents it as such. Disk Throwers have a fixed, and fairly small, range, throwing a grenade-like projectile in form of a discs. Those that don't hit a targetable entity ricochet off the ground and travel for about twice their maximum range before exploding. One can then put some grenadiers at twice their range from a stationary target (which conveniently exceeded the range of first-tier defense turrets), force-fire halfway across the distance, and hit the target with the ricocheted grenades. While not infinite range, it's still useful.
In the first Command & Conquer game, enemy units treat sandbags as impassible barriers and won't attack them directly. If you act quickly, you can use the bug to trap the enemy in their own base.
This property of sandbags could be used for all sorts of exploits. By capturing an enemy building and then setting one right next to it, you could build other things there. You could also use sandbags to prevent the AI from rebuilding lost structures since it could only do so in the exact same spot.
This is also another reason in Tiberium Wars, later patches remove the ability to build defensive structures from cranes. You can imagine the resulting terror when someone captured a structure in your base and immediately pop out 5 or so sonic emitter turrets or storm columns in the middle of your base.
The infantry selling bug allowed a clever player to complete the Nod mission 8 (which required capturing an abandoned GDI base for a Mirror Match) without selling their Nod construction yard.
Note that Red Alert 2 does the alternative with the Soviet Cloning Vats, that allow the sale of infantry with an unambiguous death sound.
It is possible in Red Alert 1 to make infantry walk on water by order them into a transport and, right as they are about to board, ordering the transport to move away from the coast.
Trying the same thing with tanks gives you a nice splash animation and one less tank. Although unusual for one unit type to have a safety measure, Infantry can actually swim.
Another bug in Command & Conquer 1 (which was removed with the last official patch) allowed the keyboard 'stop' command to cancel the selling of a defensive structure, leaving you with the infantry that spawns at the start of the selling process. Combined with the infantry selling on sandbags, this could be made into a very efficient money cheat. Even with this bug patched, a more limited version of the same trick remains possible by selling a Temple of Nod (or, in Red Alert 1, a Missile Silo) and immediately launching its nuclear missile. Since this makes the building execute the missile launch animation, it cancels the selling.
A visual feature in Command & Conquer 1 which makes infantry cut corners when walking around a walled area (since the wall graphics never actually take the whole cell they occupy) allows infantry to walk onto and over the wall, if the move command inside the walled area is given at the exact moment the soldier is technically standing on the wall.
Silos are actually unnecessary, as unused ore/tiberium could simply be used up by building something and then canceling its production, which results in a refund in cash rather than in ore/tiberium. Tiberian Sun solved this simply by making the game use the cash money before the silo-stored resource.
In the unpatched Red Alert 2, Soviets could get free infantry by building a cloning vat and constructing walls around their barracks. They would get a refund because the walled off barracks automatically cancelled the infantry's production, yet a free soldier would still appear in the cloning vats.
In Command & Conquer: Generals and its expansion pack newly constructed units spawn inside their production buildings. Normally they follow a set exit path, but by quickly giving them an order you can make them move through the building (in any direction), stop, or even shoot while still inside the building. This was heavily exploited in competitive play.
Total Annihilation: commanding long-range turrets and artillery to force-fire at the ground in front of them would force their barrels to elevate and hurl shells far beyond their usual range in that direction - albeit at much reduced accuracy.
A similar "feature" allowed submarines (normally anti-sea only) to attack land units on the coast by lobbing their torpedoes in a parabolic trajectory.
The Amiga game K240 (at least the earlier versions) allowed the player to access missile control for any asteroid he can see, not just his own. This allows you to tell the silos on an enemy asteroid to launch all its missiles at itself.
Evil Genius had a few of them, which were actually very useful if the player knew how to exploit them.
Lord Kane has one of the most useful bugs in the entire game. One of his powers forces any group of enemies to cower in fear before him, even soldiers and veterans. If you force Kane to physically attack the cowering enemies before he finishes his animation for the power, he will do so, but the enemies will still be cowering in fear, allowing you to easily kill off a few of them before they even get a chance to hit Kane.
Double clicking on a minion will make him salute the camera (and thus salute you), but, ironically, they will still salute even if they are abandoning you because of low loyalty. This is a great way to prevent important minions from escaping, since you can tag them for capture, then keep double clicking on them to force them to stop running and thus get the crud beaten out of them by everyone else in the vicinity.
Another useful bug allows one to be rid of meddling super agents indefinitely, long before discovering the methods to actually eliminate them, provided the player can baby-sit them long enough. Super agents have an easy time breaking out of a cell if they are captured, and if you leave them unattended, then they will escape. However, if a prisoner is tagged for interrogation, they cannot escape. They will wait for someone to come along and take them to the device you chose, no matter how long it takes. This includes super agents. In fact, super agents have it worse, because they will also wait for the Evil Genius avatar to arrive at the scene to laugh maniacally which, depending on the layout of your base, can take quite some time in of itself. As long as you watch them carefully, you can effectively juggle any number of super agents around your lair without ever giving them a chance to escape and cause damage.
The prison cells only have one side which is used as the entrance/exit. Everyone who wants to use the cell has to use that side, including escaping prisoners, so simply build a 2 by 1 sized object in front of the cell and they can't escape.
Lord Kane had a special move wherein he walked up to the target and used his skillz to convince them that nothing was wrong, that base they saw was all in their mind... The Good Bad Bug comes in when you tell him to do this to someone on the other side of the map. You see, once you give the order, his target doesn't move until the henchman uses his ability.
Best of all: until you kidnap the maid in one of the game's first missions, you will never be attacked, ever. You won't get any more missions, of course, but by then you are able to go out into the world and steal cash. Simply set up your basic base, rob the world blind, come back a few hours later, let the world cool off and forget about you, and get back to work several million richer.
There's one that's even better. Build a multi-sectioned strongroom, make another one, then delete the first one, and it doubles your money.
There's a really useful bug that will permanently disable a Super Agent (or anyone for that matter) with out even having to defeat them. You first need to have the Moko and The Matron in your employ. Have Moko run up to your target and use his ground-pound ability. Then have The Matron use her shock therapy ability on the target before he/she gets up. If done right the target will be locked into a loop of electrocution animation. People so glitched can still agro you minions but can't attack or take normal damage which means that you could have a pile-up of minions beating ineffectually on a guy having a constant seizure. Funny but not productive. To solve this issue a capture tag which will be effective at dealing damage. You can trap them in prison using one of the above methods or you can torture the agent with an smarts draining device and then repeat the glitch process once he's been escorted outside. The smarts damage from the shock therapy will lock the agent in "in need of assistance" and since he's already outside the base he doesn't need to be escorted. Take that John Steele!
In Demigod (lovingly ripped off and improved from DotA), one of the characters has an ability that allows him to, instead of dropping healing mana/health potions on death, drop a potion that does a sizeable chunk of damage. You can kill yourself with this potion. By doing this, you deny any enemies attacking you the kill, and you gain gold and EXP as if you had killed a demigod of your level (which you did!)
There's an interesting one in Dawn of War: Dark Crusade, where saving and reloading a game while playing as the Orks causes the engine to forget how many troops you actually have and reduce your effective headcount from 100 (or 104 in the campaign) to 24, without destroying any of your troops. While this is something of a Game Breaker, because it can be done multiple times to bring an army of 200+ Orks, it's very much in the spirit of the Ork race, who favour a green-skinned form of the Zerg Rush.
Dawn of War II's expansion has an excellent bugged skill in the form of Command Mastery. It drops the energy cost of abilities for anyone who gets the Force Commander's Battlecry buff. The thing is, it doesn't reset when the Battlecry buff fades. And it's self-stacking. I guess the Force Commander's really an excellent bard in disguise.
Normally when you play the Imperial Guard in the expansion pack if a squad is suppressed a Commissar can execute one of the squad to break suppression but in the Beta for Retribution if a squad only had the Commissar left and it was suppressed you could still have him use the ability in which he valiantly executes himself for cowardice on the field in order to inspire himself to fight harder. This is specifically forbidden by the tabletop rules.
The sad thing I can see that happening in-universe.
Ogre Battle 64 contained an item duplication glitch that would allow players to create as many weapons and stat-boosting items as needed, provided you already had at least one of whatever you were trying to copy. Given that certain powerful character classes had very specific stat requirements, which could otherwise be tricky to meet (not least because of the trademark "alignment/charisma" system), this came in very handy when a great upgrade was just a few points out of reach.
Homeworld has both the F2kzzzz and "probe bomb" tricks, which both exploit different bugs for viable strategies in the game.
The F2kzzzz glitch basically puts several different command queries for scouts together to make them flying ninjas of doom. First, you press the F2 key, which sets the scouts to evasive, making them slightly faster for a cost in firepower. Then, you press "k," which initiates the kamikaze attack. Normally, this would be lethal, but by then pressing "z" repeatedly on the keyboard, you initiate a special Up to Eleven ability for scouts that makes them even faster, so fast in fact, that they prove too agile to die. As a result, the scouts become nigh impossible to kill and trail closely behind enemy fighters, shooting the entire way.
The probe bomb trick takes advantage of the unusually wide area of effect for scuttling a probe, thereby enabling you to kill any number of unfortunate strike craft to wander in range.
Empire Earth had an interesting one involving the AI: they'd attack the first unit to attack them until the unit died or was out of sight. So send a ranged unit to attack melee soldiers, they'll follow without fighting the rest of your army currently ripping them to shreds. While less useful in later ages, what with the disappearance of melee units, it still does wonders for your self esteem to lead Alexander's army without losing a single man.
In Dune II, a building that constructs troops could be surrounded by walls or other buildings to block it off. When a unit is built in a walled off building an airlift will pick it up and drop it in a nearby open spot. If you have no available airlifts (either you have none, or all are busy), then one will come from off screen, perform its function, and leave (also occurs if you lose your last harvester). If another unit calls an airlift just with the right timing, said airlift will pick it up and bring it where it needs to go, and will on random occasions, remain as a free airlift unit (normally one of the most expensive and useful units in the game, and very high tech). This allows access to airlift units much earlier then they should be available, and for free.
The Lord of the Rings: The Battle for Middle Earth II has two great glitches, both to do with custom heroes. One allows the player to give their heroes powers from any class, by clicking from one to the other very fast (there are walkthroughs available for this). The other allows a custom hero to use the self heal power over and over, by clicking the power and then moving instantly.
In the Age Of War Flash game, units continue to be built even when the game is paused. Meaning that if your base is under attack, you can stack a very large amount of firepower hiding behind a MeatShield. A case of Awesome but Impractical, as they then move in single file towars the enemy's base.
Warcraft II had the lumber bug: having your peasants start harvesting trees then immediately canceling and building your town hall would net an extra 100 lumber. It was never patched because it actually improved the game by speeding up the slow-paced beginning of a match, and was recommended to use in all tournament games. The Updated Re-release fixed the bug but also gave every player an extra 100 lumber to start with.
In Age Of Empires I, using multiple priests to convert one computer controlled unit would sometimes lock up the AI; since it couldn't decide which priest was a greater threat, it would get within attack range and just stop.