People like it because it is LimeWire in a webapp.
Actually, scratch that -- they like it because it lets them listen to whatever the song they want to listen to, whereever they want to listen to it. As far as I know, nobody has that kind of selection anywhere else.
But I still wonder, how is Grooveshark still online legally? They let people upload their music and other people listen to it. It's basically Napster in 2012.
There is a subset of music that is not available on the Spotify/Rdio net, for various reasons. If you don't have iTunes Match/Google Music/Amazon Cloud Player with this subset synced into, what do you do when you want to listen to a song now? You might find it on YouTube, or you might find it on Grooveshark.
I thought we got past regional bullcrap in 21st century as well. But as long as all other digital music stores and streaming services greet me with "Go away, you're not allowed to listen to us from your countrty" I'm happy to give Grooveshark money.