Dog bites to people are a common presenting problem to emergency hospitals 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, the can be substantial tearing and bruising of tissue causing damage to the skin, muscle, and nerves.
Dog bites tend to have more crushing and skin trauma whereas cat bites tend to have bacteria implanted deep into the tissues. Both types of bites are dangerous.
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.