Ratskinner
Adventurer
I had a hasted dwarf fighter annihilate my balor in one round with a full attack where he scored 3 critical hits and dealt out over 200 points of damage. (in case you were wondering, we make all of our "to hit" rolls on the table in front of everybody)
I can go on with several other examples as well, but that one came first in my head.
The discussion brought to mind a paladin I once DM'ed 2e for. He had the weirdest luck with "to hit" rolls. Throw a goblin at him and he'd whiff all day, put him in an impossible situation like...
...after a protracted running battle in a drow slave camp/mine.
Me: The drow sorceress is now flying, she casts Magic Missile....12 points to the Elf Wizardess.
Wizardess: I'm down!
Illusionist: I'm out of ranged attacks!
Paladin: Augh! I don't have any missile weapons...Can I chuck my bastard sword at her?
Me:

Paladin: ::Looks around:: Another Magic Missile like that and we're all dead anyway. ::calculates:: I'll need a 19 or 20 to hit. Here goes nothing. ::rolls:: Natural 20!...Max Damage!
Me: um....she drops....dead.
...a surprise attack by a Green Dragon in a Jungle, several levels later:
Me: The huge monster crashes through the trees belching a cloud of poisonous gas that covers the whole group. Roll a save or take <some massive amount of damage>.
Wizardess: OUch! I'm down.
Illusionist: Me too.
Cleric: Whoopsy!
Fighter: Too bad you guys didn't heal me up when you....
Halfling Thief: So like...-14 is bad, right?
Paladin: I have 7 hp left...
Me: (I know it didn't really happen, but somehow, in my head, the lights dimmed and green flames erupted from behind the DM's screen.) MWAHAHAHA! Paladin, you have initiative, what do you do?
Paladin: I charge.
Me: Heroic, but futiile!...roll your dice!
Paladin: Natural 20! ...Max Damage! x2 for charging x2 for crit....umm 68 points!
Me: um... she dies.

Of course, this is a little balanced by episodes like the time he was trapped in his collapsed tent as a troll stood on top of him for the entire fight.
2e weird mechanics...but it seemed to generate the best stories of any edition, IME.