It is your choice if you want to file an insurance claim after an accident, but be cautious about making this decision. The way you go about paying for damages without insurance depends on the circumstances of the accident.
If you’ve been in a single-vehicle accident without damage to anyone else’s property, it is your choice if you want to report it. If you get a repair estimate and can afford to pay the expenses out-of-pocket, this may be preferable to increasing your premiums by filing a claim.
However, if both parties agree to settle without insurance, that is fine. If it is decided that you were at fault, you will pay for the other driver’s repairs, or vice-versa. But be warned: repairs can be expensive, and unexpected medical issues caused by the accident can really wrack up the costs.