For me:
Recently, in Wizardry 8, I went out of bounds, took a screenshot, and posted it to the Wizardry series sub forum on this website.
Not so recently, in Fire Emblem: The Sacred Stones, I got Bishop Natasha's Dark magic skill up to S rank, allowing her to wield the most powerful dark magic spells and, when attacking monsters, get triple damage from them. I also found out the hard way that, if the final boss attacks a non-spellcaster who is equipped with Dark magic, the game will freeze even if animations are set to disabled. (There's a glitch which allows you to control enemies and get their enemy-only items, and one of them (Stone) is a Dark magic spell that anyone can use and which boosts your Dark magic skill if used enough, allowing the character to use other Dark magic spells.)
I don't know if I mentioned it before in this thread, but in Might and Magic 2, I once killed the 3 Cuisinarts without winning any other battles first, and I took a screenshot to prove it.
Now, some things that others (not me) did:
There's the famous Super Mario 64 "Watch for Falling Rocks in 0.5x A presses" video; somebody has managed to play it back on an actual Nintendo 64. It took 3 tries because the run would desync. (Note that the length of the Youtube video is misleading; parts of it are greatly sped up, and the actual run takes something like 13 hours.)
In the RPG Limit Break marathon that just happened, there have been absurdly glitchy speedruns of Dragon Warrior 3 NES and Dragon Quest 5 PS2. The DW3 speedrun uses a ridiculous amount of luck manipulation, and for a while is walking around with a party with no living characters. (Also, there's a reason why the category is called Any% Major Skips.)