This is going to be a list of almost every comp that each class can play that is at least remotely viable. It's also going to contain the common name given to each comp. I'll try to list them top to bottom based on the strength and popularity of each classes comps. Hopefully this list helps out some of you who might not know what comps they could possibly be running, or for those of you who might now know what each comp is called. I'll also list the max rating of each comp to maybe give a better idea on how strong it is. Also note that the max rating of each comp is not 100% accurate due to certain teams multi-comping. Thanks to Nerdstompers.
MAGE
Mage/Feral/DiscPriest - Max rating=2861 I have recently started playing this comp and I have to say this is by far one of the best comps you can run as a mage. It has VERY strong burst, survivability, and CC. Two basic strats are to either CC the other teams healer infinitely, or to train the healer to the ground.
Mage/Priest/Rogue - RMP - Max rating=2918 Still a very strong comp. Has been strong almost every season to date. Very good control and bursty comp. Very fun to play.
Mage/Spriest/Rdruid - Shatreeplay - Max rating=3010 Probably one of the best wizard cleave comps that a mage can play. This comp brings double dispels, along with insane burst damage and control. Might not be as good next patch because priests are losing dispel.
Mage/Lock/Shammy - MLS - Max rating=2805 Although not as overpowered as it used to be, still very strong. Next patch expect to see this comp be a tier 1 comp.
Mage/Lock/Druid - MLD - Max rating=2932 Not quite as good as it used to be, but still very strong if played correctly. All 3 team members have to coordinate lots of CC to land a kill.
Mage/DK/Priest - Max rating=2702 Not sure how strong this comp is but it's definitely pretty solid.
Mage/Warrior/Paladin - Max rating 2728 Fairly strong comp with good burst potential. One of the more fun comps to run as a mage.
Other comps:
Mage/Rogue/Druid - RMD - Max rating=2608
Mage/Warrior/Druid - Max rating=2747
Mage/Rogue/Shammy - RMS - Max rating=2341
Mage/Warrior/Priest - Max rating=2646
Mage/Spriest/Rshammy - Shatterplay- Max rating=2702
Druid
Moonkin/Lock/Shammy - LSD - Max rating=2906 Probably THE strongest comp you can play as a druid, although you have to play it moonkin so this might not be the comp for everyone. This comp has massive pressure due to the fact that you and your warlock both just DoT up the entire team and do massive damage.
Feral/Mage/Priest - Max rating=2861 It has VERY strong burst, survivability, and CC. Two basic strats are to either CC the other teams healer infinitely, or to train the healer to the ground.
Druid/Mage/Spriest - Shatreeplay - Max rating=3010 Another very strong comp. This comp brings double dispels, along with insane burst damage and control. Next patch it probably won't be as good because priest are losing dispel.
Druid/Spriest/DK - Unholyplay - Max rating=3050 Although this comp isn't as strong as it was early season, it is still a pretty solid comp capable of bursting or outlasting. This comp has a ton of CC and constant pressure. Requires decent coordination.
Druid/DK/Lock - Shadowcleave - Max rating=2820 This comp was also much stronger at the start of the season than it is now. Still a decent comp, but melee cleaves can give it a bit of trouble.
Druid/Mage/Lock - MLD- Max rating=2932 Pretty solid comp as long as you and you're team have good coordination. This comp should get much stronger next patch.
Druid/Spriest/Rogue - Max rating=3050 In the right hands this comp can be very strong but it's not one of those comps that anyone can play and succeed at.
Other comps:
Druid/Mage/Warrior - Max rating=2747
Druid/Mage/Rogue - RMD - Max rating=2608
Druid/Mage/DK - Max rating=2694
Druid/Lock/Warrior - WLD - Max rating=2751
Feral/Warrior/Healer - Kittycleave - Max rating=2767
Death Knight
DK/Spriest/Druid - Unholyplay - Max rating=3050 Although this comp isn't as strong as it was early season, it is still a pretty solid comp capable of bursting or outlasting. This comp has a ton of CC and constant pressure. Requires decent coordination. Fun to play as a DK because you get tons of dispels
DK/Warrior/Pally - TSG - Max rating=2724 Fairly strong comp for a DK to run. You basically have a limited time to zerg someone down with your cooldowns.
DK/Warlock/Healer - Shadowcleave - Max rating=2780 This comp was much stronger early season but since then has got a bit weaker due to the fact that warrior teams can give you trouble. This comp might be much stronger next patch due to warlock buffs and warrior nerfs.
DK/Ret/Healer - Max rating=3053 Pretty strong comp with insane burst, durability, and CC. Can potentially global someone. Pretty good comp at zerging down healers.
DK/Hunter/Pally - PHD - Max rating=2756 A very pressure-based comp. Once you start going defensive you have probably lost.
Other comps:
DK/Hunter/Druid - TreeHD - Max rating=2716
DK/Warrior/Druid - TreeSG - Max rating=2652
DK/Mage/Priest - Max rating=2718
DK/EnhanceSham/Druid - Max rating=2743
Warlock
Warlock/Warrior/Shammy - WLS - Max rating=2959 Very strong comp. Does insane damage and seems like it has a very fun playstyle. You can swap around a lot to create more pressure. Warriors and locks have good synergy.
Warlock/Moonkin/Shammy - LSD - Max rating=2906 Probably one of the strongest comp you can play as a lock. This comp has massive pressure due to the fact that warlocks and moonkins can create a ton of aoe damage by DoT'ing up the entire enemy team.
Warlock/Rogue/Shammy - RLS - Max rating=2910 Has been a very strong and solid comp since the start of the season. All 3 classes on this team have great synergy. You can play this comp many different ways and all are very effective.
Warlock/Spriest/Shammy - Shadowplay - Max rating=3015 Pretty strong comp and I don't think it's really too hard to play. The warlock and priest can create massive amounts of pressure with ease and force the other team to have to play defensive. Also has double dispels so obviously that's a really good bonus!
Warlock/Mage/Shammy - MLS - Max rating=2805 Although not as overpowered as it used to be, still very strong. Next patch expect to see this comp be a tier 1 comp. Very control/bursty based comp.
Warlock/Mage/Druid - MLD- Max rating=2932 Pretty solid comp as long as you and you're team have good coordination. This comp should get much stronger next patch.
Warlock/DK/Healer - Shadowcleave - Max rating=2820 This comp was also much stronger at the start of the season than it is now. Still a decent comp, but melee cleaves can give it a bit of trouble.
Other comps:
Warlocks can play with almost anything
Warlock/Feral/Shammy - Max rating=2726
Warlock/Rogue/Druid - RLD - Max rating=2703
Warlock/Warrior/Pally or Druid - Max rating=2875
Warrior
Warrior/Lock/Shammy - WLS - Max rating=2959 Very strong comp. Does insane damage and seems like it has a very fun playstyle. You can swap around a lot to create more pressure. Warriors and locks have good synergy.
Warrior/Hunter/Healer - KFC (Kung Fu Cleave) - Max rating=2922 This comp is best using a Shaman healer, but also can work with a Pally or Priest. This is probably one of the best comps you can run as a warrior right now. Has insane damage and great control. Throw a few scatter traps onto the enemy healer and faceroll to victory!
Warrior/Ret/Priest or Shaman - Max rating=3017 Pretty strong cleave team. This comp brings a ton of damage to the table and you are also paired with a Ret pally so you can get freedoms to stick to your targets better.
Warrior/DK/Pally - TSG - Max rating=2724 Not really amazingly strong, but pretty solid. This comp can create a ton of pressure and if you line up some good CC with fear, strangulate, gnaw, HoJ, etc, it's very hard for the other team to catch up.
Warrior/Mage/Pally - Max rating=2832 Fairly strong comp with good burst potential. One of the more fun comps to run due to getting freedoms and having the potential to kill someone in a deep freeze.
Other comps:
Warrior/Lock/Druid - WLD - Max rating=2875
Warrior/Dpreist/Pally - Max rating=2785
Warrior/Rogue/Priest - Max rating=2726
Warrior/Spriest/Druid or Shaman - Max rating=2857