This is really an impossible question to answer, you first have to define what "Chinese" is, then you have define "what a "dialect" is. Linguists have been arguing over these distinctions for years. They cannot even agree if Chinese is a single language or an inclusive group of several distinct languages.
The simplest answer would be...lots and lots.
EMW Cultural Immersions' Chinese language camps; Where East meets West. www.emeetw.com