Sorry, I was confused when I looked at their web site. At first I thought it looked like they have a web-only version, as well as a computer version for Windows and Mac, and a mobile version for iPad and iPhone. But then I thought that what had looked like a web-only version was really just three different subscription tiers (with the lowest tier being the free plan), and that you still needed to use either the computer or mobile application with your chosen plan. So I downloaded and installed the SoundCloud 4 application for Windows, although I haven't tried it out yet. Was my first impression actually correct, that you can use the service online without installing a computer or mobile app?
EDIT: Sorry, I did indeed mean to say "ScoreCloud" rather than "SoundCloud"! Mea culpa.