How many kinds of cicadas are there? That depends on what you mean by kinds.
There are over 190 species in the U.S.A. and over a dozen in Canada. Australia has hundreds of cicadas and you can find a list of them here.
World wide, there are over 3,390 species, with new species described every year (I counted them all in this book)!
A good source of papers about new cicadas is Zootaxa.