The answer hinges on whether or not this other computer already has an iTunes library or not. In theory, if you copy your iTunes folder located in My Music (on Windows XP anyway, I don't have Vista or 7 to tell you where they are on there), to an external hard drive and put it in to corresponding location on your other computer and launch iTunes, it'll read the copied library. If you already have a library set up on the other computer it'll prompt you to replace the folder, don't do this unless you want to overwrite your existing library. If you choose to combine the libraries by importing into iTunes it will lose the playlists and playcounts. The album artwork can always be downloaded through the GraceNote service or re-added manually.