Quickest death I've seen is a close match between three dwarf fighters in different campaigns. None in the first round, but all three in the first fight.
One time the player announced that his dwarf could take three goblins on his own, and not to get in his way. Turned out there were five goblins, and someone who falls over a trip wire can be sneak attacked quite effectively.
Another time, a replacement character was a hastily rolled up dwarf who we encountered inside the dungeon. The first encounter was a mummy, he failed his saving throw against fear and fled, encountering the rather large group of hobgoblins we'd earlier managed to avoid and alerting them to the presence of intruders as he died.
The last of these dwarves was killed, drowned when a trapped section of bridge gave way as he was charging a group of bandits near Nuln.
My quickest character death was in my first ever D&D game. I'd realised that a wizard with one spell wasn't going to be much use in most fights, so bought as many darts as I could afford to throw at people. Unfortunately this was when I still went to school, and we were playing there during free periods. I was the only person going to a particular class from the group so left my wizard in the care of one of the other players. When I got back, he was dead, having gone into melee with a hobgoblin. The other player hadn't realised that darts were a type of weapon, and the only other thing I had was a quarterstaff.