I use Spotify on a number of computers, and I often login to my Spotify Premium at other people's computers.
It would be nice if Spotify remembered my Last.fm login information globally. At least set up by default, so you can disable it locally if needed. But I think full "globality" is the best solution. I'm pretty sure this is the preferred behaviour for most people.
A similar idea has already been suggested here:
Add your kudos there please! 😉