I have the habit of listening to online music. I use the following two websites for this:
Grooveshark (now off the grid): This is already a well-known service. It has paid mobile service as well though the Android app seemed to be heavy to me. I love the surveys option to gain points. Once you have enough you can enjoy a free month’s service. The collection is huge and you can have your own customized playlists. The featured new releases section is also good for having a taste of the latest music.
2. Aupeo: Hosted in Berlin, the single thing absolutely I love about this site is its international music section. It has a plethora of world music collection, from J-Pop to Italian to Spanish. It has a free Android app service which was again, a bit bulky and buggy the last time I checked.
Here’s another website primarily for Indian songs, started 18 months back and having apps for many platforms – Gaana.