Yes, you should call your insurance company after a minor accident. You should contact your insurer anytime you're in an accident involving another driver, but it's even more important to call promptly if the accident resulted in property damage or injuries. The only time it might be worth skipping a call to your car insurance company is if you damaged only your own car, there are no injuries, and property damage is minimal.
There are two big reasons you should always call your car insurance company if you get into an accident involving another driver, even a minor accident:
1. You might want to file a claim
Even if the accident seems minor at the scene, you might decide later that you want or need to file a claim. Accident-related injuries like whiplash can have delayed symptoms that don't show up right away, for example. Or, maybe a dent or scratch doesn't bother you at first, but when you find out the impact on resale value, you change your mind.
2. The other driver might file a claim
A handshake agreement at the scene doesn't prevent the other driver from filing a claim against your policy. Your insurance company is there to help defend you, either with the other driver's insurer or in court.
If you don't report an accident right away, your insurance company may be able to deny any claims you file and won't represent you in a claim or lawsuit, leaving you to pay out of pocket. Your insurance company can say your delay in reporting resulted in them being unable to properly investigate your claim, so they are no longer obligated to cover you.