Karthus could die once, and never be killed, damaged, or CC'd again. It was a bug, and even Karthus players were glad it got fixed.
Miss Fortune used to be literally uncatchable (except by Rammus & Master Yi).
The Brush on Summoner's Rift used to be A LOT different; more like the last iteration of Twisted Treeline with it cutting off all the jungle exits everywhere; you would literally never see ganks coming (unless you warded from the get go, which nobody ever did).
Tryndamere could hit for about 1800 to 1900 for 3 out of 4 attacks.