Hearthpwn

Druid: Get your Aspirants out early, for a huge advantage. Double Aspirant just gives you so much more ramp, that a normal Midrange/Ramp Druid can't keep up. For the token Druid: Get your Living Roots, Wrath and Darnassus Aspirant out early, Maintain board control and they haveno chance at all. I think the deck is really weak on it's own already.
P.S.: Watch your health, If it's below 14, make sure you have a Taunt or play Loatheb. (or heal, but usually this isn't favoured, since you really need the draw from the Lore.)

Hunter: Try to think of how you're going to get board control. And don't die. You have enough stuff to deal with their minions to keep you above 12 health by the time you've got board. Always think twice if you're going to taunt or heal. If they played Kill Command and Quick Shot already, you can easily Taunt, but otherwise healing is probably better.

Mage: Use Wrath on Mana Wyrm, Keeper of the Grove or Living Roots on Sorcerer's Apprentice and Swipe on Flamewaker. Then only Antonidas is a real threat, but if you've got board control you can easily deal with him.
For Freeze Mage, keep your Loatheb until they use Alex so they can't burst you down next turn. Make sure you don't play too much bad minions, since Freeze Mage will often just freeze your minions, not destroy them.

Paladin: Haven't faced any of these yet. I'd say you just mulligan for a good ramp and/or curve, and if it's eboladin, I guess you're doomed, unless you draw Wild Growth into double Druid of the Claw and the four Ancients. I don't know how this deck performs against Eboladin, but I suggest you to play double Sludge Belcher for Azure Drake and maybe even double Sen'jin Shieldmasta for Piloted Shredder.
Against Midrange, curve it all out nicely, and try not to use your Keeper of the Grove's, so you can silence Tirion Fordring. Paladins usually don't have anything else you have to silence, so don't waste them.

Priest: Be wary of Lightbomb and Mind Control. Those are the only real threats/game changers a Priest has. If you just curve it all nicely this is an easy matchup.

Rogue: Haven't seen one of these in a while, but I suggest you to use Loatheb if you think they can have a good Blade Flurry and just curve. That should do the trick in almost every matchup (except for ebola decks like Rush Pally, Huntard and GPW)..

Shaman: Use Wrath, Living Roots or Keeper to clear the Whirling Zap-o-matic. And having a good curve is enough to win this matchup. Currently 3-0 against them, and I won all three with ease.

Warlock: Zoo is a tricky one, since you really have to fight hard for board control. You should mulligan for early removal like Swipe, Wrath and MCTech here.
                I'm currently 4-0 against Handlock, and won them all pretty easy, but it's still a hard matchup. You need to think of all the possibilities they have (which are alot). Get a shade out early and leave it there (this is really important. Once it gets bigger than 5 health, they have no way of dealing with it, and it can make you bypass the moltens)), make sure your opponent doesn't get below 18 health, and build up a board until you can burst them down.

Warrior: Quite surprisingly, I haven't met any of these folkes. Against Grim Patron warrior, kill the Emperor as fast as you can, and keep board control. Make sure you do not play minions with less than 3 attack on turn 8 and beyond, and try to keep removal such as Wrath and Swipe for the Frothing Berserker. Do not play Ancient of War unless you're sure he has no Execute. If you can get the AoW out, and Garrosh has no way of dealing with it, you won the game.

QUICK NOTE: Always mulligan for Daranssus Aspirant and Innervate!

Druid: Mulligan for Wild Growth, Darnassus Aspirant and Innervate, and try to get a fitting curve with the ramp cards you got. For example, if you don't have the coin, Wild Growth, Piloted Shredder and Druid of the Claw is an excellent hand. With but the coin and without you just need to get the curve. 

Hunter: Mulligan aggresively for early game removal, such as Living Roots, Wrath, Swipe and Keeper of the Grove. Never keep Shade here, it's too slow.

Mage: Here you basically have two options: Either get a really good curve, or go for early game removal. You can try and defend yourself with the removal, or you can just try and get board control. Missing the early game board control isn't that much of a deal, since Mages can't do alot if you have an empty board. Against Freeze Mage, just mulligan for a good curve.

Paladin: For Eboladin, the best way is to ramp early, so you can play your taunts earlier in the game. Early game removal is not that good (except for Living Roots), since most of the minions don't die to it (Argent Squire and Shielded Minibot. For Midrange Paladin, you really want to get that good curve, and maybe keep a Swipe to counter Muster for Battle

Priest: Most of the times Priest will not be much faster then you, especially if they have no way of drawing card with Northshire Cleric. Mulligan for Wild Growth with a nice curve and Shade of Naxxramas is an always keep here.

Rogue: Have never had this matchup, but I think having a good ramp/curve is enough to win this game. Just make sure you play around Blade Flurry

Shaman: Mulligan for Living Roots, Wrath or Keeper of the Grove. If you do not have on of these, mulligan all your cards. You need to have a way to deal with the Whirling Zap-o-matic, or else you'll be dead before you can really get something big on the board.

Warlock: Against Zoo, mulligan for early game removal. (Living Roots, Swipe, Wrath, Keeper) if you have a Druid of the Claw or Piloted Shredder with an Innervate, keep it and get it out as soon as possible.
Again Handlock, mulligan for Shade of Naxxramas, Piloted Shredder and Keeper of the Grove. Do not use your BGH on a giant played on turn 4, since they'll usually just trade that in. Use both your Keepers on their Twilight Drake's and nothing else.

Warrior: Warrior does almost nothing in the early game, except for clearing your board. Try to mulligan for a good ramp, so you can get your big minions out early. Make sure they can only draw one card from the Acolyte, and try to kill the Armorsmith before they gain alot of armor with a whirlwind effect.

Innervate: Basic card in every Druid deck. Just a double coin, which helps you getting your bigger minions out early.

Living Roots: Very good early game removal, or just some saplings that help you out gaining board control early. If you're first, you can always play double Sapling on turn 1. It pretty much gets rid of every 1 or 2 drop.

Daranssus Aspirant: Kind of hard to tell you what value it has, but if you play some games with it and you draw it early, you will easily see how much value this card can get. This fits into the deck perfectly, giving it a more steady early-game, while being able to drop the big cards earlier aswell. Lovely card!

Wild Growth: Also a standard card for most Druid decks. Druid hasn't any good early game, and with this card you can basically skip 1-2 turns of doing nothing.

Wrath: Great removal card. The 3 damage is very useful against sticky minions such as Knife Juggler and Mana Wyrm, while the 1 damage and draw can also be very nice. Auto-include in every Druid deck.

Savage Roar: Basically the finisher for this deck. Usually when you have 3+ minions on board, this card can provide lethal. I am only running one, because I usually find myself stuck with atleast one of them in early game if I run two. One is enough in my opinion.

Swipe: Together with Starfall the only AoE for Druids, and since the 5 slot is already full of top tier cards, and Starfall isn't that great, Swipe is the only good AoE card that remains. That makes it an auto-include in every Druid deck. If combined with Azure Drake, it's very, very strong.

Keeper of the Grove: This is one of my favourite cards. 4 mana 2/4 body is only weak to Cabal Shadow Priest, but the ability to either Silence or Deal 2 damage is just amazing. In my opinion this is an Auto-include aswell. Every class needs a silence, and the Neutral silence cards (Ironbeak Owl and Spellbreaker) really don't fit in with Druid. That's why Keeper has so much value,

Druid of the Claw. Quite possibly one of the best 5-drop in the game. The 4/6 taunt is just insane value, since most "Choose One" cards have worst value than just the normal cards, but Druid of the Claw doesn't. The Bear Form has better stats than Fen Creeper, and the Cat Form usually also goes 2 for 1. Also an auto-include in almost every Druid deck.

Force of Nature: Combined with Savage Roar it gives you one of the best finishers in the game, but even without it, it can still win you some games, or maybe even clear the board if you really need to. Very nice card, but I think having 2 copies of it is too much. It just gets stuck in your hand as a dead card, same as Savage Roar.

Ancient of Lore: Core card of many Druid decks. The Draw two cards option is just insane value. Arcane Intellect draws 2 cards for 3 mana, making your Lore a 4 mana 5/5, which is just amazing. Also the healing can be very nice, although it gets you less value. Flash Heal for example, heals for 5, and is only 1 mana, making your Lore a 6 mana 5/5. But that's still good value. Very, very good card. If you want to play Druid, you have to craft this card first.

Ancient of War: Huge minion. Usually turns the game around, and since most Midrange Druids don't play this card, sometimes your opponent gets surprised by it, and has no way around. When played against aggro, usually your opponent's board just dissapears in it's 10 health, and thus gets insane value. I've always thought this was a great card, and I really don't see why people don't run it. 

NEUTRAL CARDS:

Big Game Hunter: This card always gets value. Almost every deck plays Dr. Boom, and if not, you can still play it as a 3 mana 4/2, which isn't good, but still provides you some board control.

Mind Control Tech. Now this is probably the card most people hesitate about, but I think it's a really great card for this deck. Since Druid doesn't have a good AoE spell, most players don't play around MCTech. If playing against aggro, this card can be played on turn 3 to get atleast something on board. The little guy just always gets value for me.

Sen'jin Shieldmasta: Very, very solid taunt. 3/5 is good against Hunter, Tempo Mage and Grim Patron Warrior. Standard and easy.

Piloted Shredder: The post-GvG Yeti. Very powerful 4-drop, which almost always goes 2 for 1, and is played in almost every deck. Can be replaced with Sen'jin Shieldmasta if having trouble with aggro, but I think Shredder itself is already quite good against aggro.

Azure Drake: Most people are probably thinking "Why Azure Drake instead of Sludge Belcher?". Well, that's because I don't really like Sludge Belcher, and I really like Azure Drake. Besides from the Ancient of Lore, this deck has no card draw, and with the MCTech and double Ancient of War, this deck is already prepared for aggro decks. With all the patrons around, the Slime that spawns from the Belcher just give them an advantage. And the Spell Damage is just so amazing with Wrath and Swipe. I really, really like the Azure Drake, and I'm not planning on taking it out.

Loatheb: For me, this is an auto-include to every Midrange or Control deck. There is just no card with the same effect, and it can either keep you alive, or ruin your opponents turn so you can kill them next turn. Since every deck runs spells, this minion always gets value. And a 5 mana 5/5 body is also great.

Emperor Thaurissan: Some people are questioning this card for this deck, but I think it gets enough value. Giving the discount to all your cards can only help you, and the body isn't that bad. Usually this card helps me getting board control, since your opponent has to kill it on their turn, and you can usually play either one big minion, or two mediocore minions.

Sylvanas Windrunner: Together with Dr. Boom the best neutral Legendary. The effect is just game-changing, and the only way for your opponent to play around it is to silence it. It is a tricky card though. Never just drop it, but always think of how your opponent will deal with it and what you will steal.

Dr. Boom: As said, the best neutral Legendary in the game, but might not be that excellent in this deck. There are already 4 really good 7 drops (All 4 the Ancients), and this is the only BGH target in the deck. I think this card can be replaced with Cenarius, and that might even be better. I don't have Cenarius, so I can't really tell :S.

Some replacements for people with a small budget:
Dr. Boom -> Any good late game drop, from Boulderfist Ogre (not recommended though) to Ragnaros, everything should be fine.
Sylvanas Windrunner -> A good mid-late game drop, such as Harrison Jones, second Azure Drake, or maybe even Faceless Manipulator or Bomb Lobber.

All the other cards are kindof hard to really substitute in my opinion, since they are either cheap, or have no possible replacement.
Other card replacements:
1x Savage Roar and/or 1x Force of Nature for an Azure Drake or Shade of Naxxramas, recommended if you either get the combo parts stuck in your hand in the early game, or if you feel like you can never combo your opponent down. Also recommended in a more minion-based meta.

1x Sen'jin Shieldmasta for 1x Piloted Shredder, recommended if you're in a slow meta, currently using the Sen'jin because of all the hunters.
1x Kezan Mystic for Piloted Shredder, recommended when not playing against Mages. Hunters will always be around, but even without Kezan the match-up should be in your favor. Druid is the worst for the hunters.

Dr. Boom for [/card]Cenarius[/card]. Dr. Boom is the only BGH-target in this deck, and the 7 spot is already full with the Ancients. Cenarius is also amazing, since it has an even bigger impact on the board than Dr. Boom has. I'm playing Dr. Boom solely because I do not have Cenarius. I think this is definitely worth to try for people who have Cenarius.

You can tech in Big Game Hunter, Mind Control Tech or Kezan Mystic for cards like Piloted Shredder, Azure Drake or the second [/card]Savage Roar[/card] (don't really recommend replacing Savage Roar though, since this deck is a bit more aggro than the previous version, but only runs 1x Force of Nature.)