How many species of jellyfish are there?

There are many. At least five species inhabit coastal waters of the U.S., and many others are found around the world.
There are over 200 species of Scyphozoa, about 50 species of Staurozoa, about 20 species of Cubozoa, and in Hydrozoa there are about 1000-1500 species that produce medusae (and many more hydrozoa species that do not).
There are over 200 species of Scyphozoa, about 50 species of Staurozoa, about 20 species of Cubozoa, and in Hydrozoa there are about 1000-1500 species that produce medusae (and many more hydrozoa species that do not).