I always wanted to this and here it is , my first of the many posts with an Indian perspective on Gadgets and Apps (Desktop, Web and Mobile), and I thought let me start by a web app as web and cloud is the future.
Grooveshark is an online music player with radio option also. The UI is simple enough and becoming a member is good as you can manage your music library online. There are lot of songs available and i found most of the latest songs available online. You can create own playlists, and manage most of the music online. The bandwidth requirements is not that high and the quality of the music is more than acceptable. Its a must for music fanatics, Radio also functions well and there are stations by genres but i found that all the music doesn't directly fit into the genre you selected, There are additional subscription options if you want the service on cellphone and they have a mobile client for just about every platform, but your iOS must be jailbroken. Its a bit pricey though at $9.99 add with that the 3g Costs in India and you are better of listening to FM, but if you are the kind who just can't live without music. Grooveshark is a great option.