You either need to save it as an .eps, which will preserve your transparency, but is not compatible with certain layout programs, or add a clipping path then save as tiff or jpg. The tiff and jpg, gif adn bmp options don't preserve transparency. Well, gif does, but it's a pain and a horrible horrible file type for photos.
To add the clipping path, the easiest thing to do is select the transparent area, then do a select inverse. Then go to your paths pallet and save it as a work path. Then save the work path as a clipping path.
Then you can save your file and the background won't be there. Clipping paths are a little confusing the first time you do them, so if you get lost, just go to the help menu. Once you get the hang, you'll be clipping right along.