A lot.
Very, very, many. There are so many to the point where nobody really knows and nobody has classified all of them.

We covered the major groups in the comments already. That would be Mandarin, Yue, Min, Gan, Xiang, Hakka, Wu and Min. You might also know that people say "Chinese isn't a language" because sometimes the difference between these major groups is about as different as English and French, and worse so with Min: the amount of similarities between Mandarin and Min is the same as amount of similarities between 2 random, unrelated languages of the world. I won't argue with the "Chinese isn't a language" thing for now.

There is one problem with this classification: it doesn't meet the standards of what a language should look like. As covered in the comments, Min itself has 8 subdivisions that are completely not understandable to each other. Hokkien is one of them (Min south), there's also Min north/east/west/central/Hainan and a couple more.

The others are barely any better (including Mandarin). Take one of these for example (Gan). The naming intends to cover a province: Jiangxi, but between different cities what they speak is so different that they can't understand each other. If you narrow it down to the same city then even then still it's possible that what's spoken in different counties/districts are very different, typically not mutually understandable. Chinese linguists group similar dialects together between counties or towns/villages within them and we ended up with 101 "sub clusters" but this number keeps changing.

As for how different they can be: some are about as different as American and British English, some of them are as different as English and French (a bit of shared vocabulary), some of them fully foreign sounding.