Until recently, not many. The Supreme Court has been very deferential to Congress for decades on the subject of the Commerce Clause. It has, for example, allowed Congress to use the Commerce Clause to prohibit discrimination and segregation in establishments such as stores and restaurants. However, in the last 20 years or so, the Supreme Court has showed at least some willingness to push back on this issue.
The most prominent example of this was in the 1995 case US v. Lopez, in which a federal law about carrying guns near to schools was struck down. The Court ruled that the act of carrying a gun near a school was not sufficiently tied to interstate commerce to be an appropriate subject of Congressional (as opposed to state) legislation.
A very important issue that may well be decided on Commerce Clause grounds in the near future is the issue of "Obamacare." The Court may have to decide whether the Commerce Clause allows Congress to require individuals to obtain health insurance.