There are various services like Last.fm, Pandora, iLike and more which allow you to play international music online without the need to download music to your computer, but there are very less alternatives for playing Bollywood music online.
Dhingana is a social platform around entertainment which allows you to play Bollywood music online, share it with your friends, think of it as a social networking platform for Bollywood music.
Dhingana though does not only limit itself it to Bollywood music and you can also listen to music in various languages which include Hindi, Marathi and Punjabi.
Overall it looks like a pretty good service to listen to all the latest bollywood music online, they also provide you with a top music list, where you can easily find the top songs.
Currently DhinGana does not allow you to download the music, but if you have a good internet connection, it is worthwhile listening to the songs online itself.