The NES version of the original Metal Gear had a glitch when you entered the computer room, if you went immediately right you would glitch into the final boss room without having to blow up the computer. This was helpful if you didn't rescue the professor (even though you KNEW you needed plastic explosives to destroy the computer, the game won't let you unless the professor told you).
In Metal Gear Solid 4, Snake reloads the long barrel / scope Desert Eagle with a magazine. However, a glitch means the magazine is inside another long barrel / scope Desert Eagle, which he duly inserts into the space occupied by the first. It helps if you exclaim "my deagle needs more deagle!" while doing this.
The exact bug works like this: At the start of the game, he is an enemy boss, and thus his theme was correctly given the property of overriding all other music when he engages in battle, like all the other bosses with unique theme songs. However, later he joins your side as a playable character, and they added the normal player priority flag, which overrides normal music, but not bosses. The problem is that they forgot to remove the boss priority flag. Player priority plus boss priority equals higher than boss priority, so he gets to override the final boss's theme. It helps that this theme is a piece of Crowning Music of Awesome.
In Mech Warrior 2, missions had a weight limit for the player's mech. This was to insure a stable difficulty - using an 80-ton assault mech in the first missions would make gameplay way too easy. However, the lightest mech in the game—the 20-ton Firemoth—had an interesting glitch: by enabling double heat sinks, removing all extra sinks, and disabling them again, their number went to -1. It was then possible to keep removing heatsinks indefinitely, sending their number way into negative digits. Since each one removed dropped the weight by one ton, it was then possible to load up the mech with the most powerful engines, weapons and insane amounts of armor, ignoring weight requisites completely. Playing with such a modified Firemoth (after disabling heat tracking from the options—otherwise the negative number of heatsinks would explode the mech from heat buildup almost instantly after mission start) resulted in you piloting a diminutive little mech capable of zipping around the battlefield at 500 kmh, blasting away 100-ton behemoths in a single volley, and effortlessly shrugging off any plausible amount of enemy firepower.
The game had an arachnoid quadrupedal Mech - the Tarantula - which was not normally available to the player, but appeared in a mission. Because the game engine was only able to handle bipedal Mechs, an ugly hack was devised by the designers in which the two forward legs of the Tarantula were actually treated by the engine as arms. Because every Mech stands upright (but immobile) even with one leg missing, but can keep walking around even with both arms gone, this could result in the tarantula losing just one hind leg and stopping cold, losing both forward legs and still walking about, or losing both forward legs and one hind leg, which would leave it staying still while hovering implausibly on the one remaining hind leg.
Mechwarrior 2: Mercenaries had a glitch in the "Mercenary Commander" campaign mode, where occasionally a mech owned by the player would duplicate weapons after being repaired from heavy damage. Obviously this was a boon during missions, but the mech could not be customized because the weight of the duplicate weapons was recognized by the Mech-Lab while ignoring the critical slots. The duplicated weapons thus could not be removed and the afflicted mech would remain overweight for its chassis.
Another interesting glitch in Mercenaries concerned Jump Jets and locational damage. If you shot out an Enemy Mech's legs, if it had jump-jets, it would try to keep itself upright using jets. Sometimes, the AI can't keep it upright, and they end up in a facedown mech, but with a living pilot and working jump jets, which they will use to try and get upright again. Which, in some mechs with exposed heads, can result in the AI commiting suicide by jetting headfirst into a building while facedown on the ground.
The Gundam Vs Series has Green Homingnote alternately "Great Homing", after Dearka Elthmann, whose Buster Gundam gets a lot of mileage out of it. To explain: when an enemy machine is near you, the targeting recticle turns red and certain attacks (beam rifles/cannons, missiles, etc) get improved homing; when they're far away, the recticle turns green and they're harder to hit. Green Homing occurs when you fire while switching targets from a close to a distant enemy, giving the improved homing to a long-range attack and letting you pull off some insane tricks.
Starsiege had a number of exploits... some of which became standard practice because they were just that good. Where do I even start?
First, there's the Shield Modulator, which focuses the shields and allows them to track a target. The shields are strengthened all around (exactly as not intended) except for a very small arc in the rear... which remains exposed even when the shields are unfocused and "closed." This creates fantastic backstab opportunities.
Second, there's the ramming physics. If you ram a shielded vehicle from head on or from behind, you get a fairly normal collision. If you ram from the side from a good enough running start, you can punt some vehicles clear across the map. AIs are even more susceptible.
Third, some vehicles have faulty or tiny collision boxes that make them less vulnerable to enemy fire... and are consequently some of the most favored rides in the game.
Fourth, splash damage has some... interesting effects against shields. The weapon's full damage rating is applied to every location the blast "hits" (rather than being weaker farther out from the center as it is against armor), making splash weapons exceptionally good shieldkillers. The EMP cannon, which deals minor splash damage, has consequently become standard equipment for every vehicle with more than three hardpoints.
Fifth, the Predator. Oh God, the Predator. By mounting a certain armor, it becomes utterly invisible to even the most sensitive radar. Combined with the aforementioned Shield Modulator hole, the Pred becomes an assassination machine.
Sixth, Landsharking. The curious physics allow players to drive their vehicles into the underside of a ramp and force them through the ground. In a HERC, this can protect your legs from damage. In a tank, you can hide your entire vehicle underground except for the weapon mounts. This is called landsharking because several of the tanks have a vertical "fin" on top of their turrets. Understandably, later-build fanmaps feature barriers beneath any ramps to prevent this.
I could go on, but you get the idea. Suffice it to say we 'Siegers should have gotten another patch or five.
If you bench a character for 2 maps and put them back in and make one kill, the kill is multiplied into over 50 (the amount decreases over tries). Also on later playthroughs, killcounts are naturally multiplied, making it hard to keep track how many kills you need for secret characters (unless you keep memo of each).
There's also few game freezing bugs, such as one of Ryofu Tallgeese's attacks. One where you evade an enemy attack and counterattack back the game might freeze for a moment, possibly no danger of game crashing though. And last if you attack Master Therion with Shining Trapezohedron in the Demonbane finale, if he counterattacks with his Shining Trapezohedron the game will freeze; this can double as Easter Egg because it's the bad result of the Visual Novel.