56 race and class combinations

Read straight out of the client's CharBaseInfo table, which is the same list the character creator uses. If it isn't here, you can't roll it.

The matrix

A tick means the combination exists. Click one for details.

Race	Druid	Hunter	Mage	Paladin	Priest	Rogue	Shaman	Warlock	Warrior	Total
Dwarf	·	●	·	●	●	●	●	·	●	6
Gnome	·	·	●	·	●	●	·	●	●	5
High Order Skyborne	●	●	●	·	·	●	·	·	●	5
Human	·	●	●	●	●	●	·	●	●	7
Night Elf	●	●	·	·	●	●	·	·	●	5
Orc	·	●	●	·	·	●	●	●	●	6
Tauren	●	●	·	·	·	·	●	·	●	4
Troll	·	●	●	·	●	●	●	●	●	7
Undead	·	·	●	●	●	●	·	●	●	6
Windshaper Skyborne	●	●	·	·	·	●	●	·	●	5
Total	4	8	6	3	6	9	5	5	10	56

Druid: High Order Skyborne, Night Elf, Tauren, Windshaper Skyborne(4)
Hunter: Dwarf, High Order Skyborne, Human, Night Elf, Orc, Tauren, Troll, Windshaper Skyborne(8)
Mage: Gnome, High Order Skyborne, Human, Orc, Troll, Undead(6)
Paladin: Dwarf, Human, Undead(3)
Priest: Dwarf, Gnome, Human, Night Elf, Troll, Undead(6)
Rogue: Dwarf, Gnome, High Order Skyborne, Human, Night Elf, Orc, Troll, Undead, Windshaper Skyborne(9)
Shaman: Dwarf, Orc, Tauren, Troll, Windshaper Skyborne(5)
Warlock: Gnome, Human, Orc, Troll, Undead(5)
Warrior: Dwarf, Gnome, High Order Skyborne, Human, Night Elf, Orc, Tauren, Troll, Undead, Windshaper Skyborne(10)

Paladin and Druid are the tight ones. Everything else is wide open.