From a Globe and Mail story about the census in India (hat tip to Michael Kaan):
India concluded its national census this week, having tallied up some 1.2 billion souls, and the last night of counting focused on homeless people – of whom there are an estimated 150,000 in Delhi alone. Getting them into the count was just one in an array of staggering challenges: how to enumerate in the dozen areas under control of various armed rebel movements, and in the 572 tiny islands that make up Andaman and Nicobar; how to train 2.5 million enumerators and handle answers in 6,661 languages.
Whoa! 6,661 languages? The Ethnologue site says it has information about the 6,909 "known living languages" in the world, and lists only 438 living languages for India (for comparison: it lists 176 living languages for the United States, 86 for Canada, and 12 for the United Kingdom).
But if you look at the entries in the Ethnologue, you'll see that most languages have alternative names (sometimes a lot of them) and most languages have recognized dialects listed (sometimes a lot of them). That's probably enough to inflate the language count by more than one order of magnitude. (It's also true that "immigrant languages" — for India, the site mentions Armenian, Burushaski, Judeo-Iraqi Arabic, Northern Pashto, Uighur, Walungge, and Western Farsi — aren't included in the count, but they're probably a small contribution to the problems of the national census of India.)
So it all depends on how you count.