Here's my short list of things that could use a good nerfing:
Druid: Force + Roar. I think the real problem is Force just because of how powerful Charge is. Druid has some strong cards but that combo is the problem.
Hunter: Oh where to start... A few high profile streamers like Kibler have basically said the problem with Hunter is that they have access to some of the best cards at every mana point. The cards I'd really look at are Explosive and Freezing Trap. Explosive just needs to be minion damage only. Freezing needs to have the mana adjustment component looked at. Many times adding 2 mana to a minion cost, effectively, kills it. A piloted shredder is really great at 4 mana. At 6 mana it's a bad play. Animal Companion is another one to look at. Every possibility is under cost at 3 mana but Blizzard has justified this because of the RNG component. I know it's selective bias and it's only 33.33% but it sure seems like Huffer comes out more than the others (especially for Face Hunters). Now I think nerfing all 3 of these cards might be too much but these are the 3 I'd look at.
Mage: Let's re-evaluate Freeze again. As others have said fuck Freeze Mages. The one good thing is that they are hard countered by Warrior. And as Famm said, an Alexstraza nerf might be enough since their whole strategy is, Trump voice, Delay! Delay! Delay! until they can hit you with Alex and follow up with burn.
Paladin: Fine as is. They're going to lose too many staple cards from Naxx and GVG that, if anything, they're going to need help from the xpack.
Priest: We're back to really slow control Priests again. Yay... Luckily slow control Priest was never all that popular. They lose a ton of stuff though. Dark Cultists, Shrinkmeisters, Velen's Chosen, Vol'jin and Light Bomb. I'd really like for Blizzard to move away from the "thief" play style but that seems to be where they want their niche to be. It's just not fun to play against at all when your stuff is constantly stolen and used against you. I've said it before, many Priests decks have no win conditions. They simply play to not lose. And that's terribly frustrating to play against. So on one hand they're going to need help but on the other hand it doesn't take much to really make them incredibly annoying.
Rogue: Oil Rogue is gone since they lose Oil and the sticky minions they relied on to utilize oil properly. I see a lot of people who try to keep Miracle alive with Auctioneers but since they were nerfed it's a lot harder for them to go off. I think after Standard they will be fine as is and possible need help. I'd really like to see a good Tempo or Mid-Range Rogue come back but the class just doesn't seem designed for it.
Shaman: They're going to be hurting again. Mech Shaman is gone. Aggro Shaman will need to be reworked but the loss of Crackle might be a death knell for them. They lose a lot of burst with that.
Warlock: Thank God they lose Imp-Plosion. 4 mana for 4 damage and 4 1/1s was stupid (Selective bias again but I NEVER see anything other than that when I'm playing against them). I don't think Warlocks are going to need any nerfs but I also don't think they're going to need any help either. Zoo will always be a solid concept for them.
Warrior: I honestly don't know. Control Warrior might become a Tier 1 deck again. The problem is that they are combo oriented but their combos are very easy to pull off compared to other classes. I think any change to them could push them too far in one direction or another. I think playing against them the worst part is the constant armor. You don't need to do 30 damage to them. It's a lot closer to 50 or 60. But if you make changes to armor than you radically change the class.
Neutrals: The usual suspects here. Leper Gnome and Knife Juggler are both really powerful for their cost. Based on what they've said in the past I wouldn't be surprised to see Ironbeak nerfed too. I think we're going to see even more Defenders of Argus again and Azure Drakes (an already popular card). I fully expect Alex to be tweeked. And, finally, I know they love the Giant concept but I still think they could be reworked.
Finally I am VERY happy to see Antique Healbot be sent to the scrap heap. I think it was a mistake to give every class that much healing. And it was absolutely bonkers for decks like Hand Lock who wanted to get their life really low for cheap Moltens and then heal right back up with a Healbot.