One of my favorite movies of all time is Chameli, starring Kareena Kapoor and Rahul Bose, directed by Sudhir Mishra, and released in 2003. For those of you who are into the occassional "aaaart pilm" - I highly recommend it and give it 4 stars. If you have never watched a Bollywood movie, and can only watch one, it would have to be this or Sholay.
There are actually very few song scenes in the movie. Here is a snippet from the film when Kareena Kapoor "sings" Bhaage Re Mann.
And here is a snippet from AishFan, an IMDB user:
This movie is definitely a breakthrough in Bollywood cinema in terms of the story and the approach to telling it. The entire movie takes place in just one night. It is interesting to see how a family values, extremely wealthy man spends a night with a prostitute. Beginning with his prejudice, he slowly grows to accept, protect, and, one can even say, love her. It took an entire movie summed up in an extremely brief "climax" to perfectly convince and portray the theme that 'It doesn't matter what the backgrounds, gender, etc. are; there should just be love.'