Many Windows Media music stores know this concept of "primary rights". The computer you use for downloading the music gets the primary rights, so that computer will be able to not only play the music, but also burn it to CD or copy it to a portable player. Even if you have the right to transfer the music to more than one computer, all the other computers can only play back the music - they can neither burn it nor copy it.
With iTunes, it's a lot simpler, just as wataru said: "Either a machine is authorized or it isn't."
You can always authorize up to 5 machines and on all these computers, you can play, burn and copy the music (to iPods).