Mage has Counter Spell that counters spells (it's a trap). It used to be an alright spell pre-GvG but now with so many mechs running around with Spare parts Counter Spell gets played around really easy. I have still won a few matches with Counter Spell in certain match ups but overall I can't recommend it.Maybe it goes without saying, but man I'm starting to get ticked with how good starting cards can really spell doom for your game.
Especially when the enemy starts with a balance of instant minion destroying cards at little cost. Got torn apart.
Any class have anything that counters counters?
There's a minion (forgot the name) that destroys Trap cards. Also Priest has a card that damages Deathrattle minions which is useful against some decks.
Really depends on what type of counter you are looking for. Stuff like Loatheb is a good counter to some decks as well.