Yo.
Let's fuckin' talk about Pokemon (particularly Gens I and II).
So, everyone knows about Missingno, and how you can use Missingno to get "infinite" (technically a finite number but it's a fucking huge number so who cares) master balls and rare candies (or whatever other item you want). And everyone knows about the Mew glitch.
But let me tell you, there is so much more you can do with Gen I glitches. The Mew glitch, for example -- there exist variants of this glitch that'll allow you to encounter any pokemon in the game's code. Version-exclusives? Yup. Evolutions you can otherwise only get by trading? Yup. Glitches? Yeah, you could also wind up with one of those. But if you know what you're doing, you can get absolutely any species that you want.
But wait, there's more!! Whatever species you choose will spawn, by default, as a level 7 pokemon. But, this level can be altered by using stat-changing moves like growl to lower or raise the attack stat of the last pokemon of the 2nd trainer that you fight while performing the glitch (no, I'm not making this up, Gen I glitches are fucking weird). So, if you use growl on your opponent 6 times, the pokemon that spawns at the end of the glitch will be at level 1. Now here's the fun part: There aren't supposed to be any level 1 pokemon in the game. The lowest you'll ever find in the wild is level 2. Because there are no level 1 pokemon, the exp counter for them is glitched. Which means that if you put a level 1 pokemon in battle, and raise its exp by just the right amount? It'll jump straight to level 100.
So, putting the two together, this glitch can be used to get yourself a level 100 Mew. Or Alakazam. Or Porygon. Or Missingno. Or LM4. Or whatever the fuck else you want.
Gen I also has a glitch that allows you to temporarily walk through walls (which, yes, can be performed on cartridge copies of the game, without using gamesharks or anything of the sort). Its usefulness is limited, though, since it wears off when you walk through a door.
There are also a lot of minor glitches in Gen I that can be used to skip quite a bit of the game's story. Marowak's ghost in Pokemon Tower? You can get past it without a silph scope. The Team Rocket grunt blocking the door to Silph Co? He can be glitched out of the way long before he's actually supposed to move.
Now *cracks knuckles* let's talk about Gen II.
On the surface, Gen II is more polished than Gen I, but its glitches can get a lot crazier if you know what you're doing.
Firstly, there's a very convenient cloning glitch in Gen II. A very similar glitch technically exists in Gen I, but it's a lot riskier, as screwing up can mean losing your entire save file. The Gen II cloning glitch is much safer in this regard. You might get a glitchy clone every once in a while, but they're usually easy to release, and, well, it's certainly a lot better than losing your entire save file. The glitch clones can lead to some really fucked-up results if you hang onto them... but this is a thread about useful glitches, so I'll save those stories for another time. :P
There's also a glitch in Crystal that lets you play as a female trainer with the male trainer's color palette, or vice versa. ...There's really no usefulness to this glitch, I just find it kind of amusing. :D
Now for the interesting stuff: the coin case glitch. The coin case glitch is often treated as a fun-but-not-really-harmful-or-useful glitch, as the easiest-to-perform variant of it simply causes all the colors of the game to glitch out in some sort of weird, trippy display (which also reveals full-color versions of Ho-Oh and Lugia on the title screens, implying that they weren't always intended to be silhouettes). However, the coin case glitch can be used to do so much more. In fact, you can use it to do virtually anything. Like, you can use it to drop a pokemon off at the day care and then turn that pokemon into a Celebi (as well as, similarly to the Mew glitch from Gen I, anything else you might want). You can also use it to cause the game to display a custom string of text (before crashing shortly after). The variants on this glitch are a lot more complicated to pull off than the Mew glitch, though. The Mew glitch mostly just involves battling different trainers and sometimes using specific attacks on their pokemon in order to achieve the desired result. The coin case glitch will ask you to walk in a specific path in a specific location, deposit specific quantities of specific items into the PC, have on-hand specific species of pokemon that know specific moves and have specific nicknames, then use the pokedex to play the cries of specific species... Yeah, it's really convoluted. But if you do everything correctly, you can practically reprogram the game to do damn-near anything, so, that's pretty cool.
