Beginning today (Tuesday for me, since I'm on the East Coast) at noon PDT, Blizzard will be offering free character transfers from a selected high population realm to a lower populated realm. This offer is scheduled to run until Nov. 4 at noon PDT. Here's the information straight from Blizzard poster Bornakk:

In the event that these realms meet our transfer goals before the scheduled end date, the transfers to that realm will be disabled. We highly recommend that if you are planning to transfer that you do so at your earliest convenience. No characters will be eligible for these free moves once the transfers have been closed.

Once the transfers open you can begin your transfer by visiting the Character Move page located here: https://www.worldofwarcraft.com/account/character-move.html.

The full list of realms can be found after the jump.

Source A (PvE)
Silvermoon
Aggramar
Alexstrasza
Proudmoore
Whisperwind

Destination A (PvE)
Korialstrasz


Source B (PvE)
Zul'jin
Area 52
Medivh
Thrall
Doomhammer

Destination B (PvE)
Terokkar


Source C (RP-PvE)
Moon Guard
Argent Dawn
Feathermoon

Destination C (RP-PvE)
Sisters of Elune


Source D (PvP)
Tichondrius
Kil'Jaeden
Mal'Ganis
Arthas
Mannoroth
Blackrock

Destination D (PvP)
Azshara


Source E (Oceanic PvP)
Frostmourne
Barthilas
Jubei'Thos

Destination E (Oceanic PvP)
Dreadmaul