I'm feeling very glad to announce you that Google has launched its news Web app called "search online music service" ,under this you can freely search and Listen Online latest Hindi mp3 songs in India legally.
To make this thing happen Google collaborated with three digital music providers called In.com, Saregama and Saavn., which have rights of thousand of songs and also provide legal authority to listen Bollywood Movie tracks – ranging from old and new Bollywood hits to Indian classical music.
For searching songs you don't have to go through registration or subscription just visit Google Music India and you will get same search engine like Google search engine as shown Below and just put the name of Hindi song which you want to search and hit search and you will get link of song to Listen it freely
As Google provide you already Thumbails of the movies which are latest so it get easy for you to search Music.And you can listen latest Hindi movie songs online with new Google India music portal.
Note:Google Music is only providing Hindi Mp3 songs and latest provide others soon