You could daruis pull while teleporting.

Nutcracko

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.

Brand was useful at one point

Quite a few trolls would spout about how League of Legends was stealing from Dota.

how could I forget that certain champions also started with stat bonuses to Crit hit chance and dodge as well. Speaking of which TF's passive instead of gold per kill was scaling crit hit chance at what, 5 / 6 / 7 % I believe xD

Jax had a passive dodge

deathfire grasp use to do %dmg on each spell cast (like the blackfire torch) but was instantly removed for being op on certain chapions

Cho'Gath used to not actually speak words -- he would just growl and stuff.

Katarina's base model had blue hair and was basically Mercenary Kat.