Your insurance could go up on you or they could cancel depending on whose fault it was. You probably should decide what your deductible is and whether damage is more.
If you are involved in an accident with another, and you don't report it and then the other person sues you, your insurance company could deny coverage.
It's okay not to report accidents to your insurance company as long as you don't expect payment from them. Just make sure you file a police accident report.