In my 40 years of driving I have always found that reporting it to the police immediately is a good thing. When the police respond, you have the best witnesses in the world to what happened even though they may not have been there at the exact moment of the accident. They are trained to extract what happened by talking to the people and observing the situation.
I can't tell you how many problems I've seen when people don't report it. The two involved people will stand there, each admitting their part of the guilt and go back home, talk to a friend or lawyer and then completely change their story only remembering that you admitted guilt.
The things I tell people to remember:
1. Don't admit guilt
2. Only talk to the other party to exchange insurance information
3. Call the police
4. Ask people if they witnessed the accident
5. When you get home write down your story while it's fresh in your mind