If you are on one of the servers named below you can now transfer your character to sever listed beside it.

Blackrock → Bloodscalp
Icecrown → Azjol-Nerub
Deathwing → Stormscale

In the near future these realms will be available for transfers:
Frostwolf → Frostmane
Ner'zhul → Crushridge
Proudmoore → Dragonblight
Silvermoon → Draenor
Archimonde → Firetree
Kil'Jaeden → Boulderfist
Tichondrius → Dunemaul
Doomhammer → Perenolde

Check out Blizzard's new Character Transfer Page for more information