Not all car accidents need to end up in lawsuits. In fact a very small number of them actually go to court and there may be even more that never get reported to either the police or insurance companies.
If you're involved in a car accident it's not automatically assumed that you'll soon be involved in a lawsuit. The first thing to do if you're in an accident is to make sure you're okay. If you have questions about your physical health then do not get out of the car but wait for help to arrive. If you're fine then you should check on the other involved parties.
Some people are quick to get mad or upset about an accident and if you're clearly not at fault it might be hard not to get upset. But remember that getting mad won't help and it may actually make things worse. Try to control your emotions and handle it in a businesslike manner to ensure all your bases are covered.
If you have a camera on your phone then start taking pictures of the damage, the license plates of involved vehicles, the surrounding area and anything else that may be important. If you don't have a camera in your phone, buy a disposable one and keep it in your car just in case.
If the damage is slight and to both vehicles and there is question about who's really at fault, you and the other party may both decide to take care of your damages yourself rather than dealing with insurance. If someone is obviously at fault but they don't want their insurance to go up or to find out then something can still be worked out between the two of you but you should instantly get it in writing.
If it's an involved accident and no one is sure who exactly was at fault or you feel there will be a dispute, you should call the police immediately. It's not your job to negotiate with the other party and if you feel they're not being entirely forthright or you're a little wary, then use the police to bolster your future lawsuit or your case with insurance companies.