User blog comment:Vahldeer/Team Composition Talk/@comment-3450702-20121025160205

Most team comps want to accomplish reasonable amounts of:
 * Initiation power-at least 1/2 skills (Skarner ult, ashe ult, alistar W-Q, Malphite ult etc.)
 * Poke power-stuff like Jayce Q+E, Nidalee's Q, Xerath's stuff, Kog Maw's R
 * Mobility-blinks, movement speed buffs etc. to be able to follow up an initiation or escape from theirs, example: ezreal E, Lee Sin's Q,W.
 * CC- single target or multitarget, you want to balance this out with damage, stuff like Nautilus and Maokai sport lots of this
 * Burst- Akali, Veigar, Ahri... most AP Carries have this, if you can eliminate a member from a fight almost instantly it's a huge plus.
 * Sustained DPS- usually the AD's role, basically deals the same amounts of damage throughout the fight
 * Tankiness/Damage soak- think Mundo, Udyr. Stuff you can't walk by easily to get to the carries, but are hard to kill.

Now, since this doesn't quite answer your question, more to the point:

You want to have the AoE in fights to be able to control an area that they are punished for staying in, forcing them out and breaking their lines; you want the burst to kill their carries; you want the CC to protect yours; and you need some sustained damage to kill everything.