Warrior:
----- Protection: The best tank in the game, hands down.
----- Arms: Extremely strong in PvP. Source of the only 50% healing debuff in vanilla. Grab a pocket healer and you're unstoppable. Alright for PvE dps.
----- Fury: *Once you get geared* Extremely strong PvE dps. Very, very gear dependent, but once you get going, you'll be up there with Rogues and Mages, plus you'll be able to offtank in a pinch.
(As a Warrior, you are very gear dependent, and leveling will be hell unless you have a main character to feed you gear... but any Warrior will tell you, it's worth it.)
Paladin:
----- Retribution: Very self-sufficient. DPS is noticeably lower than other classes/specs, but you have very powerful utility to more than make up for it in 5mans and PvP. One of the very few specs that can give a frost mage a run for their money in PvP.
----- Protection: Very good for tanking 5mans, but not really viable for raiding unless you are overgeared. More than enough for dungeon leveling, though.
----- Holy: The most mana-efficient healer in the game. Arguably the best tank healer for raiding. Incredibly sturdy. Best PvP healer.
(As a Paladin, your blessings and offheals are incredible, and you'll be able to provide extremely powerful defensive utility.)
Shaman:
----- Elemental: PvP powerhouse. PvE, acceptable dps with strong utility... nobody will come looking for you but you likely won't be turned away, either.
----- Enhancement: See above. A string of windfury crits can bring down anyone, but it's quite RNG.
----- Restoration: Very powerful raid healer. Quite good for PvP as well. Strong damage for a healer.
(As a Shaman, you'll always bring strong utility in the form of totems and offheals, and offensive purges are a powerhouse in PvP. You can self-rez to help )
Hunter:
----- Marksmanship: Strong damage and brings a nice buff. Good for middle-of-the-road gear.
----- Survivial: Best for raiding with high-end gear.
----- Beast Mastery: Absolutely incredible for soloing and leveling. Great for low-geared PvP.
(As a Hunter, you will across-the-board have an easy time leveling and PvPing against most classes. However, the skill cap is rather high. You have a very niche role for raiding in Tranq shot, so you can get a spot rather easily compared to other pure DPS classes, as long as you're hit capped.)
Rogue:
----- Assassination: Great for PvP. Tons of burst damage and control.
----- Combat: One of the most powerful PvE dps builds in the game. Not much more to say.
----- Sublety: Tied with frost mage for the best control specs in the game for PvP.
(As a Rogue, you'll have an easy time leveling in a PvP environment, and always bring high damage.)
Druid:
----- Balance: Not that great in vanilla. Damage is alright, and utility is strong, but you'd only be brought for your buff.
----- Feral: See above for DPS(Cat) spec. For tanking(Bear), you're in the same boat as the Prot Pally: More than enough for dungeons, and you can do some raiding if you're overgeared, but you'll never be picked over a warrior.
----- Restoration: Outstanding healers, both for tank and raid healing. Interestingly, one of the best 1v1 specs for PvP, if played as hybrid cat/resto spec.
(As a Druid, you are inherently powerful in PvP due to your mobility, offhealing, and self-healing. Battle rezzes are great too.)
Priest:
----- Holy: Arguably the most powerful healer in the game, very well-rounded. Not much else to say here. You don't have the HoTs of a druid, or the mana efficiency of a Paladin, or the zzzz chain heal raid healing prowess of a shaman, but you are the most flexible healer, and can put out some serious HPS. Decent off-damage when needed as well.
----- Discipline: Kind of a niche spec, worth having one around for Pain Suppression though.
----- Shadow: Not the best for PvE dps, but your auto-raid-healing and shadow weaving makes having one desirable. However, an absolute monster in PvP, capable of melting any spec in the game, and laughing while you do it.
(As a Priest, you'll always be able to bring some off-healing or off-damage, and fort is a great buff. Mana burn and mind control are a lot of fun!)
Warlock:
----- Affliction: Amazing for leveling, PvP, and raiding. Infinite mana. Regarded as the best warlock spec for everything, I think.
----- Destruction: I'm pretty ignorant about this spec. I'm under the impression that it's inferior to affliction.
----- Demonology: Soul link is great for PvP. Not sure why else you'd pick this over affliction.
(As a Warlock, you'll bring very high dps and utility in the form of soulstones and SUMMONING!!!!!)
Mage:
You're an asshole. You do the most damage, have the most control, beat 99% of people in pvp, free food and water, can teleport to where you need to go...
Ok, but seriously.
----- Fire: Tons of damage. Lots of it. Rolling ignites are serious. But, you can't do MC as Fire! And you're actually not that great at pvp.
----- Frost: Still buttloads of damage. Arguably the *best pvp spec in the game*, right up there with Shadow Priests.
----- Arcane: Ever wanted to blow someone up instantly with a single button press? This is the spec for you.
(As a Mage, you'll get... everything the opening joke said. It's all true.)