Akali and talon can get fed pretty quickly against lower skill players. They require you to have a bit of skill with the character and knowledge of when to jump into a fight though.

I've only played morde a few times, but when I get decently fed I can just sit in a teamfight pretty good, same for rammus although it's been awhile since I've played rammus. I think morde has the potential for a penta, & can push (especially with the ghost he gets from his ultii if it kills)
My boyfriend plays AP amumu to carry his team or to just burst out any champs (a tanky ass xin for example can be bursted by ap amumu) & he just pushes alone to win if his team can just hold for the most part because if he dies he just respawns kills 1 or 2 then pushes & pushing eventually wins lol so yea xD

Poppy is the best imo for 1v5s but Nasus and Jax can all do extremely well.

Singed for sure. Almost everytime i spectate a game with Singed in it, he is the one that turns the game around. He just has so much health and resistance. Plus he can throw weakened enemies back into the fight or slow their get away. It all depends though if you build him right or not.

Singed, teemo, and shen can carry.

Shen is the easy to get fed up and he can turn a team fight right a around by ult on the one getting force by the other team.

Katarina with her ability to kill and her passive which allows her to have cooldown reductions. Even with a crappy team, as long as they can take hits for you, an ace should be easily achieved almost every team fight if you play her well. Nonetheless, if the team is too noob keeps feeding and cannot push even with an ace, there is not much chance of winning no matter who you play

morde
get your wota and abysel septer and you are painful
get a zhonas and you now take little damage form their AD carry during the 3 seconds before they switch sides as a ghost

for some reason when I was lving I carried hard core with teemo (ohe) I cant think of any reason other then his global passive making the other team play stupid and fight me one at a time (mostly) leaving the rest of my team to do whatever

nasus for the win.....