You can transfer a very sizable amount of gold, on a maximum level character.
Along with a lot of items, in your bags and such.

The neutral AH will either take 15% of the final sales value, or must be watched very carefully to ensure no one snipes your auctions if you list them for virtually nothing; the listing fee is immaterial, as it is refunded if the item sells -- which it will every time, when you are transferring items to yourself.
Not sure if it was changed in Cataclysm, but in WotLK there were four neutral auctioneers in the game: Two in Booty Bay (downstairs in the house by the half boat + by the bank), one in Gadgetzan (only building that goes underground), and one in Winterspring (basically across from the inn).