Spyro Year of the Dragon: speedway glitch.
Now, this one is particularly destructive, as it removes the ability to collect the race egg from the specific speedway affected by it. As far as I'm aware, it only affects the original NTSC copies of the game. To trigger it, enter a speedway, and then leave without getting the egg from the race. Save, then restart the game. Now you can never get that egg. It only happened on the midday speedway for me, and I was able to get to the bonus level after collecting/completing everything else possible and using the warp cheat.
Stardew Valley: babies spawning in walls.
Now, I don't know how to trigger this one, but whenever I adopted a child in the game, the day the kid arrived they would get stuck way into the top left corner of my house. I believe they would also spawn there randomly upon a new day, but it's been a while since I've played.