There are many great Indian films the answer to this question is very subjective to the interests of the person writing the answer and of course the interests of the person who asked the question in the first place.
I would assume that you are probably a person not very familiar with the Indian Cinema. So I would like to recommend movies that are not only great but also explain a lot about the Indian culture and Indian Cinema aswell.
In the history of Hindi Cinema, 50s was the decade when the rights of women, labor, and issues of social justice and extreme poverty were a major subject in many hit movies. These movies have a huge impact on the Indian society. The storylines often revolved around poor people resisting rich people and fighting for social justice. This main theme continued for a next few decades until the 90s when it started dying slowly.
In 00s and 10s Indian cinema is now much more commercialized and the storyline of poor people struggling against capitalist villains is dead now. The new storylines are showing the struggle of Indians towards richness of the economic boom.
I have tried to make the list of the movies that were significant in shaping the Indian cinema and influencing the Indian culture.
1. Awaara (1951)
2. Devdas (1955), based on Sharat Chandra Chattopadhyay's novel of the same name and directed by Bimal Roy, Dilip Kumar played the role of Devdas in the movie. Devdas has been made several times and it is one of the epic love stories of Indian Cinema.
3. Mother India (1957) The epic story of the struggle of an ordinary village woman who lived a difficult life raising her children without her husband while working in their farm land and saving it from Sukhilala, the village moneylender who collects wealth by giving loans to villagers and occupying their properties and jewels if they fail to payback. Mother India has a huge impact on Indian culture and society. It is one of the most popular films in India.
4. Mughal-e-Azam (1960) an epic historical romantic melodrama that immortalized the story of Anarkali and the Prince Saleem. This film is considered one of the greatest Indian movies ever. The songs, costumes, dialogues, lavish production mesmerized Indian audiences. Even today it is one of the most watched Indian movies of all time.
5. Sholay (1975) Read about it on Wikipedia, this movie is considered by many as the greatest Indian film ever made. It was a huge success at the box office and the characters and dialogues from the movie are still part of the Indian popular culture.
6. Deewar (1975)
7. Amar Akbar Anthony (1977) This film is one of the formula films of late seventies. The storyline begins with three brothers getting separated due to terrible circumtances in the childhood and the family gets reunited in the end just before the climax. It had comedy, romance, action, an emotional story line, melodrama, and so much more.
8. Karz (1980) This movie is important because it is the first of the commercially successful movies based on the theme of Reincarnation.
9. Mr. India (1987) an ordinary man who runs an orphan house from his own pocket suddenly finds a gadget that turns him invisible.
10. Maine Pyar Kya (1989) This film is significant as it gave birth to the romantic 90s. The storyline is basically the same old love between a rich guy and a poor girl. But it has beautiful songs and after a whole decade of action movies this film was welcomed by audiences as a breeze of change.
11. Hum Apke Hain Kaun (1994) One of highest grossing Indian movies of all time. This musical romantic comedy is significant as it started a change in the Indian cinema. Until this movie the Indian cinema never paid attention to lavish weddings, orchestrated and choreographed wedding rituals. This movie started many new trends like lavish productions of wedding songs, bridal dresses, jewelry and showing the beauty of Indian culture through weddings and other ceremonial rituals.
12. Dilwale Dulhaniya Lejaynge (1995) This is the highest grossing Indian film ever. It is also the longest running and the most successful Indian movie of all times.
13. Lagaan (2001) historical film that depicts the beginning of India's love with the Cricket and also its discomfort and struggle against the British Raj.