I am seriously alone amongst my friends in this, but I simply adore Bollywood movies, especially the musical comedy variety, though some of the dramas are really fantastic, too. But the musicals almost always have a surreal quality to them that won't let me just ignore them, and the dance moves by gorgeous people to the great music...well, these films are simply a feast for the senses! Peter understands my love of Bollywood enough that he's given me two FABULOUS collections of music, one only available outside the U.S. BTW, the songs are NOT sung by the actors/dancers. The singers are stars in their own right in India.
You say you're interested but not sure what to reach for first? Give Monsoon Wedding a shot. A lovely film with comedy, a couple of quite dramatic sub-plots, and it's not all sub-titles, which may help ease you into appreciating these wonderful films. Or, in the same vein, Bride and Prejudice or Bollywood Hollywood are both terrific starting points. You really can't go wrong with anything from directors Deepa Mehta or Mira Nair.
If you prefer to try a drama, I highly recommend Dil Se from 1998. Starring the incredibly FINE (pant, pant) Shahrukh Khan, this film left me completely stunned with an utterly unexpected ending.
As usual, Wiki offers a lot of information on Bollywood worth reading, and a very helpful list of top films, too.
Trailer for Monsoon Wedding
Trailer for Bollywood Hollywood
Bharati - Bole Chudiyan (song from Kabhi Khushi Kabhie Gham, or "KKKK" its short title in Hindi)