Introduce a web app.
One way Spotify can edge out its competitors is because, in 2013, we're all about having access to everything we own, everywhere we go. That's why we use Google Docs and haven't touched Microsoft Word in ages. We're up in the sky, chilling in the cloud, baby.
If you head over to a friend's house and want to play that dope mix you recently made, you can log into your Spotify account and it'll be there—if they already have the app on their computer. If not, you're out of luck. For now.
Spotify actually has a web app, that's currently in beta, on the way. When you can log into the service from any browser, like Facebook, expect the service to get even more popular.