1) Back when I was in high school, my gaming group decided to take a session off from our regular campaign and play something else. Our DM pulled out Legends & Lore (that edition's Deities & Demigods) and told us to pick a character from the Arthurian myths. We were going to attack Asgard.

Naturally, the big names (Arthur, Merlin, Lancelot) went first, but I actually owned a copy of that book and picked my favorite. The Green Knight who (among other things) was immune to melee damage.

I ended up going against Thor. It went back and forth for a while, and I barely held my own until our DM rolled a 1.

By house rules, that meant he had to roll again to see if he broke his weapon.

That's right... I was one roll away from BREAKING MJOLNIR!

(We ended up losing when Morgan Le Fay betrayed us and switched sides).

2) At one of my first Arisias several years ago, I signed up for a GURPS game in which the party played the crew of a Klingon Bird of Prey. For reasons I can no longer recall, I ended up the ship's gunner and optimized my character for that.

We went up against a Federation starship. The captain ordered me to fire a warning shot. And somehow, in a million-to-one chance... I hit the reactor core dead center.

So much for THAT encounter

3) At a later Arisia, I played my one and only session of PARANOIA and managed to execute my entire group for treason... during the mission briefing.