How many religions are there?

The answer depends on how you count them. If you are interested in recognizing the historically important varieties of religion that have been listed in encyclopedias, the number is on the order of thousands. If you are interested in recognizing the number of distinct religious beliefs held privately, you would have to count the historically unimportant and unrecorded eccentricities of probably millions of people.

By the way, Guide to the Gods lists more than 17,000 gods, and it is seriously incomplete (Marjorie Leach, 1992, Santa Barbara CA: ABC-CLIO [sponsored by UCLA]).