The first problem you run into when trying to identify some good Indian movies is the fact that Indians, between them, speak some 1,500 languages. According to the Census of India of 2001, thirty languages are spoken by more than a million native speakers each. When you apply that to mass entertainment, conflicts emerge. Ask your taxi driver for a recommendation and the answer given will vary with his language preference.
I found a list of recommended Indian movies online a few years ago and showed it to an Indian woman who was studying in Adelaide. She had previously been employed in television somewhere in Mumbai. She was outraged by the list because they were all made by the 'wrong people.' I don't speak any Indian language; I just get by with the subtitles, so all the in-fighting is wasted on me. I just want an interesting story, preferably with readable subtitles.
One of the best Indian movies I have seen, Lagaan, revolves around a cricket match between untutored Indian villagers and the cream of the local British garrison in 1893. The film was the third-ever Indian film nominated for an Academy Award. It can be found on the list for The 100 Best Films of World Cinema. The soundtrack is listed on Amazon.com's The 100 Greatest World Music Albums of All Time.
Below we have the trailer and a video outlining the making of Lagaan.
Meanwhile, if you get the chance, try some of these Indian films. (I don't know what language they are in, sorry.)
3 Idiots (2009)
Kabhi Khushi Kabhie Ghan (2001)
Munna Bhai MBBS (2003)
Rang De Basanti (2006)