The hardest champ that I've tried to play would have to be Anivia. Tried her one free week, and just struggled to really use her effectively. Mostly because my wall positioning was a cry in shame, and unless your lane opponent derps hard, it can be difficult to land her stun. I also found Talon rather difficult to play effectively, but I think last played him when I was new to the game, so that might have contributed to that perception.
I'm personally surprised to see Rumble mentioned so often - I tried him out last free week, and absolutely dominated with him. The only lanes I had trouble against were solo-laning against a very aggressive Graves/Teemo and Singed/Darius (that double pull.. >.<). Otherwise, just bully the opposing laner relentlessly, and punish them when they come in and try to CS. You do need to manage heat though, but other than when a chaotic teamfight breaks out, that isn't overly hard to do. The short CD on your skills, and cycling them smartly takes care of that.
Also, I don't find Ori that hard to play - I am usually able to win lane with her, but you do need to put up with a very passive early game, and manage your mana carefully. Leaning ball positioning, and how to effectively zone, and to land her skills takes time, but can be rewarding when done well. She doesn't offer the same amount of burst as conventional AP carries, but she offers a lot of utility, and with the right team comp can absolutely wreck the enemy team. You do need to farm lots though to stay effective.. and I mean lots. That said, she's great fun to play, and is on free week now, so definitely give her a try