For PvE:

This depends on yoursetup... After a lot of thinking about teams/dps/buffs and debuffs, I went the following route:

2 paladins (one protection specced, the other healing or Ret, depending on how hard retribution gets nerfed)
Logic: One paladin can be used as a main tank, the other can be used as an offtank or a backup healer. Between the two paladins you can run two different auras at once, and have two separate sets of blessings (e.g. Blessing of Kings +awesome stat bonus and the Intellect blessing). The main tank is required for multiple obvious reasons (I hope), and the offtank is generally required for many situational bosses. 2/3 tanks is the ideal end-game "raid" setup, and I'll discuss that below.

1 Druid (feral specced atm, girlfriend plays her)
Logic: The druid offers a myriad of added values to your team, and can fill a variety of different rolls (even the MT roll, if the situation calls for it). Some of the added (and quite often missed bonuses) of the druid are: increased spell crit chance (moonkin), heal over time spells, moderate crowd control (cyclone - and before you knock me on this one, read the word MODERATE), resistance buffs (Gift of the Wild).

5 Shaman (Elemental)
Logic: DPS, DPS, DPS, non-cloth based DPS. Having characters that are not cloth based tends to lead to a generally higher survivability rate. Although this isn't always true, with the added heals, totems, and group/ now RAID wide buffs that the shaman provide, having multiple shaman is never a bad thing.

1 Priest (holy)
Logic: The main healer of the group. The healer provides buffs and protection for the entire raid party. The healer generally sits in the back of my team, just tossing heals when needed. Having a true 'healer' makes any raid situation much easier (think: Circle of Healing, which is often touted as overkill for raids, etc.)

1 or 2 Mages (arcane or fire):
Logic: Glass cannons, but very, very effective at dealing damage. Increased mages = increased dps, plain and simple. Also useful for their arcane intellect buff.

If you look at the above scenario, you'll notice that I listed a total of 11 characters (again, the g/f plays one). If I had to limit it to ten, I'd probably just stick to one mage. You're going to have enough sustained dps (so long as you can keep everyone alive), to fight nearly any encounter. Also, you're going to have almost every single buff in the game at your disposal, at any time. Combine this with potions and gear, you'll be all set.

Best,