First I'd like to state Corki, though most don't agree with me on this, he is quite stacked. Start with his flash bomb and you'll be set at early levels and easily farming mobs while keeping your distance, he has a nice skill that makes fleeing a simple task, and on top of this he gains spammable missiles (of which when you raise crit hit rate and crit damage) can do well over 1k before you even hit level 16 in a match. The only issue he truly has is his lack of mana, but that's what the item shop is for now isn't it?
Second is Fiddlesticks... Such an easy character to play... I mean seriously... you have to be stupid to fail with him. He has a massive amount of AoEs, fear (which helps you get out that final attack without getting any damage dealt to you), oh and did I mention that one of his techniques stops skill useage? So those bothersome Yi whores can get owned nice and quick. The same technique that blocks skills is also amazing for farming, it hits multiple targets repeatedly for high damage. Another one of his attacks drains health and restores your own for equal amount. If you raise Fiddle properly you can use it to not only take down an opponent fast, but absorb all of an attackers damage making it seem as if you were never attacked in the first place.