Comps I've Seen:
AoE (Amumu + Kennen + Kata + Sona + Corki)
Protect the Kog (Kog, Orianna, Nunu, Cho'Gath, Alistar)
Poke Comp (Taric, Caitlyn, Morgana, Jayce, Maokai)
Late Game Stall/HyperCarry (Karthus, Tristana, Sona, Jax, Skarner)
Split Push (Anivia, Shen, Soraka, Sivir, Jayce)
If you're n00b, go AoE, it's by far the easiest comp to play. The rest of the comps rely strongly on having map control and positioning to take towers, baron, and other objectives for free. A lot of them require huge patience and strong disengaging. Remember, winning the teamfight and losing towers will lose you the game.