I had two accidents last year, all my fault. (unlucky!) But no major damages on other cars. I told them I prefer to resolve this privately. After they had the estimate done (if they want to repair, sometimes they just want some cash for compensation), I paid them after negotiations if that's possible. (Since it's your fault, you don't have much for bargaining. But give it a try.) Upon payment, I signed an agreement with the other side which stated when, where, and brief descriptions of the accidents, and how the accident was finally resovlved. You may add other details. But I don't feel it would cause me trouble in the future. Going to the insurance company will definitly cost you much much more and will drag on for years. Accidents happen when people are a bit careless. So drive carefully. But once it happens, pay and get it over.