There are many cards one can play around and that one should expect, knowing the capabilities of all classes and the common tactics is necessary for high-level play. All that would be far too much for a single answer here, but there are a few devastating plays that are useful for new players to know.
I've restricted my list to the most dangerous cards or combos, only those that can completely turn the game if you are playing into them unaware.
- Flamestrike : 4 damage AoE for 7 mana
- Blizzard: 2 damage to all enemy minions for 6 mana
- Equality (2 mana): Changes health of ALL minions to 1. Usually combined with Wild Pyromancer or Consecration (4 mana, 2 damage to all enemies) to clear the board
- Blessing of Kings (4 mana): +4/4 to 1 minion. The threat of this card means that leaving a weak minion alive (even a 1/1 token) can be risky.
- Paladins have less reliable removals on strong minions, and therefor a Big Game Hunter (kills on 7+ atk) can be worth to be prepared for
- Unleash the Hounds: Summons 1 hound for every enemy minion (3 mana). Usually combined with Starving Buzzard (5 mana) for card draw and/or Timberwolf (1 mana, +1 attack for beasts) for damage.
- Explosive trap: Deals 2 dmg to all your minions when you attack your opponent's hero.
- Deadly shot: 3 mana, kills random minion. Opponent will try to create a situation where you only have 1 high-value target (and no other minions) before casting to guarantee a winning trade.
- Lightning Storm: 2-3 AoE damage for 3 mana, especially dangerous as Shaman has a totem with +1 spell damage
- Bloodlust: 5 mana. +3 attack to all minions (caster side only) until end of turn. Dangerous because it means that any board with a lot of minions (including totems) is potentially lethal.
- Auchenai Soulpriest + Circle of Healing. This combination deals 4 damage to ALL minions on both sides.
- Holy Nova. 2 damage to all enemies, heal all friendly characters 2 for 5 mana
- Brawl: Destroys all minions except one randomly chosen one for 5 mana
- Whirlwind: Deal 1 damage to all minions for 1 mana
- Swipe: 4 mana. Deals 4 damage to 1 target enemy and 1 damage to all other enemies
- Starfall: 5 mana. Deal 2 damage to all enemy minions or 5 damage to one enemy minion
- Being a class with many strong taunts, a game changer can be an Ancient of War (5/10 taunt) when you're out of removals. Use your removals and silences wisely when dealing with their 3/5 and 4/6 taunts.
- Force of Nature (6 mana) + Savage Roar (3 mana). 4 + 4 + 4 + 2 = 14 damage. The distinction of 3 separate 4s and a 2 is important when calculating damage through taunts.
- Hellfire: 4 mana. Deal 3 damage to all minions on both sides. Especially dangerous if opponent already has Nerbuian egg or Voidcaller in play.
- Twisting Nether: 8 mana. Destroy all Minions on both sides. Especially dangerous if opponent already has Nerbuian egg in play.
- Shadowflame: 4 mana. Destory a friendly minion and deal it's attack damage to all enemy minions (strong with Ancient watcher, it's a flamestrike in that case)
- Deadly poison + blade flurry: 5 mana, dagger > deadly poison > attack(hero or minion with more than 3 hp) > blade flurry, deal 3 damage to ALL enemy characters, includes hero, it's a very strong and flexible board clear combo and also deal 6(or 3) damage to the hero. Sometimes combined with assassinate blade instead of dagger, deal 5 damage to ALL enemy characters, but requires more mana and more card.
- Deathwing: Destroy all minions, 12/12 for 10 mana. (Almost never played, I wouldn't worry about this one)
The list is incomplete, feel free to add to it (this post is community wiki)