Thousands. Every municipality in my area can have their own sales tax and can change them whenever they want. For Texas alone that's ~1,220 potentially different sales taxes which can change at any time. Its not an impossible to keep track of thing though, plenty of organizations do it and most payment processors will essentially handle it for you. But its not exactly easy, aggregating all that and getting it all right in the first place is a good bit of work.

There are thousands of different sales tax rates in the US that change multiple times per year.

Each city, county, state and other things like metro transit districts, water districts and school districts can all contribute to the sales tax rate paid by an individual at the point of sale.