I'll update this post as I remember but for now, these are the movies that have a rewatch value for me. Basically, I've seen all these movies more than once.
Dil Chahta Hai. Bromance between three friends and their romantic stories. We have an arranged marriage, an older woman-younger man story and the third is the typical young love story.
Main Hoon Na. Action. Romance. Comedy.
Kuch Kuch Hota Hai. Friends turned lovers.
Kal Ho Naa Ho. Friends turned lovers and a 'Taming of the shrew' type story.
Hum Tum. It borrows a little from When Harry Met Sally but not too much. One of my favorites. It's follows a couple as their relationship evolves over a number of years.
Saathiya. About the ups and downs of young love.
Lagaan. Extremely long but I thought it was worth it. About imperialism and of course, has a romance.
Mr & Mrs Iyer. This is not a Bollywood movie per se since it's in English but a pretty great film. The first 30 minutes are really hard to get through but most end the movie feeling that the pleasure is worth a little pain. A story of a couple that meets on a fateful bus ride.
Socha Na Tha. Arranged married turned to love. My description sucks but I really liked this movie.
Jab We Met. About a couple that meets on a fateful train ride.
Rules: Pyaar ka Superhit formula. A girl follows her grandma's advice to nab her dream man. Sounds kinda dumb but I found it really cute
Monsoon Wedding is also not a Bollywood film as it's in English but I think a good movie for someone trying to test the waters. It's set around a girl's arranged marriage.
Hum Dil De Chuke Sanam. I really liked the second half but it's about the story of a girl who falls in love, loses her love and chases after that love but through this journey, discovers what real love is.
For something a little grittier
Company about gangsters and stuff. lol... I saw this movie a long time ago so I can't even describe it in detail but I remember loving it.
Salaam Bombay is a less romanticized Slumdog Millionaire.
1947 Earth is about Partition.
Kannathil Muthamittal is in Tamil and deal with issues of political unrest in Sri Lanka and also adoption.
These are just a few that I particularly enjoyed but there are many more that are worth one watch. I might update this list at a later date.