Agents Of Mayhem is a buggy little number that I've played this far. I've fallen through the world quite a number of times, which isn't fun considering the repetitive gameplay I've had to endure.
My favourite "glitch" is grabbing Wheatley out of a surprise appearance during one of the early tests. He doesn't do anything, but it's Wheatley, so it's okay.
There was this really old kids math and reading computer game with a minigame where you had to make triangles with the specified dimensions. One of them was a triangle with a=2 and b=5. And no matter which direction I made it, THE GAME SAID MY MATH WAS WRONG. I remember being incredibly frustrated (I was like 8 playing this) because the character I was drawing these stupid triangles for was super smug about my apparent "error". He was all like "Oohooo, not quite there kiddo, we wanted THIS triangle, and you made THAT triangle." HE EVEN REPEATED THE EXACT DIMENSIONS I GAVE and I was like "HOW IS THIS INCORRECT, YOU LITERALLY JUST REPEATED YOURSELF YOU DAFT AI"
If there was anything that would make me rage - and I'm usually pretty level-headed - that would be it.
Looking back at it, I think one of the reasons I was so upset was that this was a kid's game, where the difficulty is supposed to be pretty darn low XD And then the AI goofs and decides to make you feel stupid by being stupid as well X_X
That's the problem with edutainment games. They tend to have 'false difficulty' due to mediocre programming done for it. You see it a lot for the old Disney games for PC, back in the mid-90s (though obviously they aren't the only offenders). Watch any videos that talk about those kinds of games and that often comes up.
There was a glitch I found in Okami where Amaterasu's head ended up weirdly elongated and flat during a cutscene. It looked like her head had been chopped off. It was still there when I got out of it, but it fixed itself after I jumped around a little bit. I found a glitch in mystery dungeon explorers recently where if Grovyle is using dig while you're in a dungeon together and you move in a way that he'll follow you, he'll just follow you as if he isn't underground and it will cancel out the move. I don't think it does that with any other Pokémon, but I'm not sure.
My favorite glitch is from rune factory frontier. You have to beat the first boss in a VERY specific manner and when you do it right it clones consumable items. but if you do it wrong it will delete them instead. Other notable glithches (probably more on topic ones) includes my Pokémon go avatar turning into a green or white blob when I put the app in the background, or the original rune factory mount glitch that would allow you to access misty bloom cave outside of winter or in the same game the glitch where I would just phase through monsters while fighting them.
*One time in Pokémon Emerald, i found a weird glitch which allowed me to walk through walls. I went all the way to Ever Grande City.
I've been digging for one of these glitch threads. You know how I am, just breaking everything in every game I play. (Semi) recently the beta for Stardew Valley multiplayer was released. The purpose of the beta is, of course, to try to find any of the remaining bugs in the game so they can be fixed before the game is officially released. The game's creator apparently said before releasing the beta that he thought it was mostly bug free. A friend and I broke it within 20 seconds of playing. My friend created the server and I joined in. While I was doing character creation, he came into my cabin and swung a scythe at me. Somehow that forced me out of character creation and each time he swung the scythe at me, it would spam me with the "Go to sleep?" prompt. Once he stopped, I was locked out of character creation. I tried leaving the server and logging back in and the game instantly crashed.
I played Spyro a few weeks ago and while I was, I encountered a few glitches. In Spyro 2 I accidentally got a Super Jump while attempting to charge into some flame-able gem barrels. They broke and sent Spyro up into the air (the same height of a Double Jump, not up to the skybox or something extreme like that) while he flailed like he was falling. While fighting Gulp, I lost Sparx and got hit- but didn't die. I couldn't pause the game, and was stuck fighting Gulp till I got hit again and finally died.
Glitches? Now that you've said it, I have so many games that have glitches, mostly in Pokémon GBA Games.
Whenever I play Generation 1 Pokémon game, I always (okay not always) use the Mew glitch, only thing is that it is hard to level up to the rest of my team's levels (even if I was just in Cerulean then)