I think everyone is aware of Spotify by now and if you are not, you probably don't live in the UK, France or Scandinavia. Shame for you really, because Spotify is really part of the digitial music revolution.
Hosting an incredible 10 Million tracks and growing by about 10k songs every day, Spotify can really give any serious music collection a run for it's money. A subscription allows you to play songs on the go, download them on your device and listen to them offline for 3 month and stream from mobile devices. A subscription costs currently £10 a month, which is not much if you spend that much on CDs each month anyways.
Unfortunately Spotify is not yet ready to replace CDs. Not all artists are on Spotify, in fact I often find artists missing. Most notably Led Zeppelin and The Beatles to name just two of the big ones.
Nonetheless, you might not want to store music on your phone, you might not want to stream it from home or you just don't have the song you want to listen to at all, maybe you fancy something new and need a suggestion or you want to listen to the new album by your favourite artist... Spotify probably gets you what you crave and thus makes it on the list of my top ten Android apps.
The app itself as the typical Spotify look and feel. You can create playlists on the go, listen to playlist you have on your account and download these playlists to your Android. It runs pretty stable in the background and also scrobbles to Last.fm.
Do you need anything more?