So I am going to take waht Nomax said, and Kinda ignore it. Half if it isn't true at all. and in all honesty, i hope you don't read it.
Hunters: Hunters are finally scaled down to where other classes actually have a very good chance of beating them. As OP as they are in Lower brackets, they are not as OP in the 39 bracket compared to others. They are absolutely necessary to have at least 1 on D due to flares. However the 39 bracket is definition the stepping-stone from where hunters no longer have the OP-ness that they seem to have in lower-brackets.
Rogues: With Premeditation available @39, rogue's burst dmg is a lot scarier than before. As long as you have over 3k hp w/ rum unbuffed then rogues should be a big issue for you. FCs/Healers normally will run around with Green whelp armor or/and lots of Nature Resist. This is the best way to counter a rogue. Other than that, rogues are definitely one of the most overpowered classes in the 39 bracket.
Paladins: Every spec is viable at 39. Prot paladins make great FCs and even decent DPSers(however no where near as good as a ret paladin). There are only two viable healing classes @39 and one of them is a Holy Paladin. Holy paladins(if played correctly) will never oom and are great healers. However if u dont run around with green whelp armor, you might find urself vulnerable. Ret paladins are without a doubt a very strong class @39 due to Sacred Shield. If you focus on stacking nothing but AP, then your SS will absorb more dmg(which is what you want). And more AP comes with harder hits, and since ur spec allows your Crusader Strike to already have a high crit chance, crit is not needed. Not to mention they have the speed boost
Warriors: Warriors are a very viable FC class @39, they have just as many abilities and utilities as a Paladin; which makes their Skill-Cap as an FC just as high as a Paladins if not higher. Due to incombat charge, most people would say that Prot is the only Viable spec to play as a DPS. IF you do plan on going Prot DPS(which you should imo), do not worry about stacking Crit, stack straight up Attack Power. Even if you do try to stack crit, you may be lucky to get over 15% crit(which in all honesty isnt that much). If you stack straight up AP then add the extra AP you get from vengeance, you'll be hitting like a truck.
Mage: Fire is the most viable spec. Where as Frost may have the higher skill cap than Fire, fire mage will win vs a Frost/arcane mage. As a Fire mage, their main priority is to stack Int/Crit. Since they have Cauterize, they cannot be "2shotted" by rogues, which just makes it a pain in the butt to kill

. Not to mention they also have Stuns, AoE CC, Speed Boosts, and can cast Scorch while running. If you plan on playing as a Fire mage, you will notice quickly how OP this class/spec is.
Warlock: This is one the least viable specs, but I have seen players in Cata pull this spec off. However you will rarely see any in your BGs(US). With proper Fearing, and good usage of ur DoTs and pet abilities; you might be able to top the DPS charts and keep ur healers alive; but u r very squishy and in all honest you lack a lot of survival skills that all the other classes have gotten @39.
Druid: The only spec that I would suggest you not to use is Resto, not even Resto FC. Feral has gotten some abilities that has increased their skill-cap pretty well from 19-29. However in all the classes, specs, etc that are available @39, Balance has the highest Skill cap out of all of them. Similar to warlocks tho, they are quite squishy even while in moonkin form. But don't let that stop you. Balance is very viable spec to play @39 and will require a lot of patients and determination to figure out. Don't let anyone tell you that boomkin isnt viable, other than being squishy; Boomkins has every utiltity/ability to make them necessary to have in any game.
Priests: Similar to Holy Paladins, Disc Priests are a very viable spec to heal in and is without a doubt necessary. Disc Priest's Bubbles can almost absorb just as much as an AGM @39. Shadows priests gear exactly the same way as a Fire Mage. Stack INT/CRIT, due to Shadowform and priest bubbles; they can easily survive and beat any 39 rogue. Don't let a Shadow priest fool you, in the right hands they are just as deadly as a Fire Mage.
And last but not least
Shamans: Shamans are an interesting class indeed. Do you Nature's Swiftness, A Resto Shaman technically could be a viable class since they can technically survive a rogues 2shotting BS hits. Not mention they also have Nature's Guardian. But compared to priests or a holy paladin, a shaman's heals will never come close to theirs. If you truly wanted to play a shaman at their prime, play them @29. Now Ele and Enhancement shamans are very fun and very interesting. Due to having Magma totem @39, having a Shaman on D is absolutely necessary in any situation. Ele shamans are very viable to play. Due to having a 5 second CD on Wind Shear, Thunderstorm, being able to use magma totem, being able to cast Lightning bolt while casting(similar to fire mages), and even able to throw decent offheals, they are without a doubt a very viable class to play @39. Lets also not forget Enhancement. Enhancement is a slightly squishy, but as soon as Windfury/Mongoose procs; Enhancement shamans start hitting like Trucks. Not to mention, they are the best class to pair up with a Hunter. a Hunter's Flare combined with an Enhancement Shaman's Magma Totem(with the extra totem reach from their spec), it not only stops Rogues from getting out of stealth but it also puts them in combat so that they have to wait several seconds to go back into stealth. Put a healer with the two of them, and they become an unstoppable force @any choke point. Shamans have one of the highest skill-caps @39. Definately not an OP class, but without a doubt necessary to have in any BG.