Most people would not associate Identity Theft with an auto accident; however, your personal information could be at risk during the exchange of information.
The Department of Motor Vehicles http://www.dmv.org provides a checklist of what to do after an accident.
To protect your identity give out ONLY the following information:
Your vehicle’s make, model, year, color and VIN;
The name of your insurance company, as well as your;
Agent's name and phone;
DO NOT allow your license or registration to be photographed; and
DO NOT provide your address or contact information to other drivers, passengers, or witnesses.