Pet bites to people are a common presenting problem to emergency rooms around the country.
Bites are dangerous for two reasons. First, the bites are often loaded with tons of bacteria that are essentially "injected" into your flesh increasing the risk of infection. Secondly, bites can cause substantial tearing and bruising of flesh, muscles and nerves.
Dog bites tend to have more crushing and skin trauma injuries whereas cat bites tend to have bacteria implanted deep into the tissues. Both types of bites are dangerous. Cat bites are actually worse because the smaller puncture wounds might not look as bad initially, so they are mistakenly ignored.
If you have been bitten, call your physician or go to your local emergency room.
For more information on pet bites, please read The Danger of Pet Bites.