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Indian here, so will do a quick list of my favourites according to their genres. This list also serves as a recommendation for people looking for good movies.
Romance
Lootera A masterpiece. If you love slow romantic movies with gorgeous settings.
Politics, Drama and Satire
Swades Loosely based on a true story, and made me care about my country. The most patriotic movie ever that I have seen, that was devoid of any bloodshed or action.
Jane Bhi do Yaaro A brilliant satire. The dark comedy continues to be relevant even for today.
Hazaron Khwaeishein Aisi Centred around the Naxal movement. Largely in English.
Satranj ke Khiladi The genius Satyajit Ray's Hindi venture.
Gangster and Cop dramas
Satya A mirror image of nineties Mumbai underworld. A raw and gritty film. Also, the film that changed the way dialogues were written in Bollywood movies. Up until this movie, dialogues were largely influenced by Urdu, but this movie started the pure Hindi language trend.
Gangs of Wasseypur 1 & 2 The bloke who co-wrote Satya wrote and directed this two part series, that was loosely based on the mining mafias and politicians of Jharkhand and Bihar. Brutal and realistic. Is available as a seven part series on Netflix, but I would suggest watching this is in movie format.
Ardhya Satya Old indie cop drama. Again fairly realistic.
Sadak Sort of an adaptation of Scorsese's Taxi Driver, that was elevated in quality because of the villain.
Thrillers
Andhadhun Coen-esque dark comedy and thriller.
Raazi Based on a true story about a 20+ year old spy who got married into a Pakistani family and helped India win the 1971 war.
Johnny Gaddar An Indie thriller.
Being Cyrus Dark tale with an anti-hero in English.
Talvar Based a true double murder incident.
Comedy
Mr India A proper children's film on the age old invisible man plot and a memorable villain.
Dewana Mastana A laugh riot.
Hera Pheri Another laugh riot.
Chalti Ka Naam Gaadi A classic staring the beautiful Madhubala who had several offers from Hollywood, but she turned them down.
Delhi Belly A Guy Ritchie like comedy available in Hindi and English.
Feminist or Female oriented films
Mirch Masala A cult classic.
Lipstick Under my Burkha A brave modern work exploring female sexuality and rights.