Free character migration is available from July 1st till the 7th which gives you a week to decide if you make the move or stay put. As usual, Blizzard could well end the migration when their desired faction balance on each realm is achieved.
So who can move and where? If you're Alliance and currently playing on the European realms Burning Legion, Grim Batol, Ravencrest, Sylvanas and Silvermoon (PvE) you can move to the Horde-heavy servers of Magtheridon and Vek'nilash. Meanwhile if you're Horde, and on Al'Akir, Kazzak, Magtheridon and Stormscale, you have the option of transferring to the Alliance-dominated realms of Burning Blade, Neptulon, Tarren Mill and Trollbane.