The World Christian Encyclopedia of 2001 counted 33,830. (For a breakdown of these numbers, see this Fact Sheet, which also pulls data from the World Christian Database mentioned below. Here’s a tidbit you’ll find in the fact sheet: There are 242 Roman Catholic denominations! And another: It is estimated there will be 55,000 denominations by the year 2025, which does not say much for ecumenism.)
The World Christian Database carries “extensive data” on 9,000 Christian denominations.
The Hartford Institute for Religion Research says that the 2006 Yearbook of American and Canadian Churches lists 217 denominations, adding that it’s a “very tough question, because it depends on how a denomination is defined.”
We can therefore conclude that 1) there are a lot of Christian denominations, and that 2) there are so many that they are not easy to count.