What Happens if you get into a car accident and do not call the police?

If you exchange information, then nothing will happen. If you get into a car accident and flee, then its considered a hit and run.

Additional: Some states REQUIRE that collisions exceeding a certain dollar amount be reported either to law enforcement or the DMV REGARDLESS of whether the drivers exchange information and/or settle amicably between themselves or not.

In the UK nothing. You only need to involve the police if there are injuries or deaths, obstruction to the highway or physical or potential danger to other road users/pedestrians.