This depends on the original copyright of the audio file. If you have the rights necessary to listen to any type of music, you can legally do so as you please.
Youtube
In Spotify.
You tube
One can legally listen to the songs of A.R. Rehman online at Saavn website. One can also download their application which is available for all platforms. This is the easiest way of accessing his songs.
No, it is not illegal to listen to Hindu devotional songs online if you are listening to a legal site. It may help you feel better throughout your day.
Create a "T.M. Revolution" station on Pandora
You can legally listen to Bollywood songs online for free on YouTube or any other video hosting website they might be uploaded on. Also check free audio streaming services like Spotify and grooveshark.
you can search them on youtube.com and other places just like normal music
You can listen to Khmer songs online on websites such as Khmer Komsan and SDAP Online. You can also find songs the songs listed on the video streaming website YouTube.
You cannot download MP3 songs of copyrighted material for free legally. iTunes and many others sell songs for $0.99. You can use services like GrooveShark to listen to thousands of songs online, but the files must be purchased to transfer to your iPod.
You can listen to online songs in MusicIndiaOnline.com
You can download songs by going to the iTunes Store.