Currently the following cards and sets are legal for Core:

Worldbreaker Block
Sets: Worldbreaker, War of the Elements, Twilight of the Dragons
Crafted: (5) Crafted 1-12
Badge: (5) Badge 1-12
Special Releases: Class Starter Decks (2011)
Promotional: Cataclysm Collector's Edition, (5) Holiday 1-6, (5) Class Promo 1-13

Aftermath Block
Sets: Throne of the Tides, Crown of the Heavens, Tomb of the Forgotten
Raids and Treasure Packs: Dungeon Decks
Crafted: (6) Crafted 1-9
Justice: (6) Justice 1-12
Special Releases: Champion Decks
Promotional: BlizzCon 2011 Card, (6) Holiday 1-4, (6) Champ Promo 1-10

(5) Badge 1-12: Amulet of Dull Dreaming, Celadon Pendant, Pendant of Quiet Breath, String of Beaded Bubbles, Band of Bees, Band of Secret Names, Ring of the Battle Anthem, Twined Band of Flowers, Bedrock Talisman, Core of Ripeness, Fluid Death, Soul Casket

(6) Justice 1-12: Melodious Slippers, Moccasins of Verdurous Glooms, Rock Furrow Boots, Treads of Fleeting Joy, Floating Web, Haunt of Flies, Heavenly Breeze, Viewless Wings, Crystalline Brimstone Ring, Deflecting Brimstone Band, Soothing Brimstone Circle, Splintered Brimstone Seal

(5) Crafted 1-12: Crawling Claw, Scimitar of the Sirocco, Staff of Ammunae, Chalice of the Mountain Kings, Clockwork Gnome, Staff of Sorcerer-Thane Thaurissan, Queen Azshara's Dressing Gown, Bones of Transformation, Highborne Soul Mirror, Snaggle, Soggypaw, Violet Proto-Drake

(6) Crafted 1-6: Fossilized Hatchling, Fossilized Raptor, The Innkeeper's Daughter, Nifflevar Bearded Axe, Puzzle Box of Yogg-Saron, Wisp Amulet, Ultramarine Qiraji Battle Tank, Voodoo Figurine, Ring of the Boy Emperor

Cataclysm Collector's Edition - Jacob Blackcrest, Kirox Butcherblade

(5) Holiday 1-6: Red Rider Air Rifle, Kwee Q. Peddlefeet, Krazal the Eggregator, Searing Scorchling, Swift Brewfest Ram, The Horseman's Horrific Helm

(5) Class Promo 1-13: Bolvar, Highlord of Fordragon Hold, Burly Berta, High Commander Halford Wyrmbane, Jaina, Lady of Theramore, Leeroy Jenkins, Deathlord Jones, Garrosh Hellscream, Plainswatcher Taro, Saurfang the Younger, Kor'kron Warlord, Thrall, Warchief of the Horde, Babagahnoosh the Grumpy, Fordragon Hold, Kor'kron Vanguard
BlizzCon 2011 - Hogger Monster Hero

(6) Holiday 1-4: Winter Veil Disguise Kit, Apothecary Hummel, Spring Rabbit, Ahune the Frost Lord

(6) Champ Promo 1-10: Aurius, Bath'rah the Windwatcher, Eris Havenfire, Hemet Nesingwary, Keeper Remulos, Klannoc Macleod, Lord Darion Mograine, Lord Jorach Ravenholdt, Mor'zul Bloodbringer, Rhonin