I think the numbers are somewhat disputed. The People's Linguistic Survey of India says there are at least 780, with ~220 having died out in the last half century.[1] The Anthropological Survey of India reported 325 languages.[2]
The discrepancies are made particularly tricky because of the somewhat ambiguous distinction between languages and dialects.
I'm not an anthropological linguist, so I can't say with any authority. I only listed two figures there, but there are many more disputed figures.[1] There are a lot of difficulties classifying languages in India because the line between language and dialect can be tricky to pin down.
The discrepancies are made particularly tricky because of the somewhat ambiguous distinction between languages and dialects.
[1] http://blogs.reuters.com/india/2013/09/07/india-speaks-780-l...
[2] http://books.google.com/books?id=VjGdDo75UssC&pg=PA145