In addition to the normal transfers, a large block of PvE servers have the option to get a free transfer to a new realm, Garrosh.
Garrosh is a PvE EST based US realm. It's been placed in the Emberstorm battlegroup.
Blizzard's announcement lists next Wednesday, January 14th, at 6:00 p.m. PST as the cutoff date for the transfers. However they will close the transfers early if they meet their internal quotas. Transfer early and transfer often. You can begin the transfers via your account management page at worldofwarcraft.com.
The complete list of eligible transfer realms after the break
Source A (PvP)
Thaurissan (Horde transfers only)
Destination A (PvP)
Source B (PvP)
Destination B (PvP)
Source C (PVP)
Mal'Ganis (Horde transfers only)
Destination C (PvP)
Aggramar (Alliance Transfers Only)
Alleria (Alliance Transfers Only)
Lightbringer (Alliance Transfers Only)