Rhapsody and Rdio are pretty close. They're like Spotify but I believe both have browser based access. Catalog is a little smaller but I hear plenty of people say they prefer them over Spotify. None of them competes with Grooveshark's catalog, because a huge chunk of Grooveshark's catalog is not there legally.
Yeah Rdio is pretty great, and they give artists access to an under-publicised affiliate program allowing them to earn money off the audience they drive to the platform. Solid iOS app. Personally my favorite of the streaming services.
I'd also keep an eye on eMusic. It's more geared towards downloads, but they offer a lot of really great editorial content for discovery plus they offer multiple streaming radio stations for members. They've got smart people so I think they might make a surge in features.
A lot of people are into MOG.com as well. I have issues with their CEOs attitude towards licenses and how the money goes to creators, but otherwise the catalog is strong and they offer solid access across multiple platforms.