Most people at one point or another will have to deal with a car accident of some kind. There is a specific protocol to follow after a collision. You should contact the police, see a doctor and call your insurance agency.
However, the other driver may want to bypass all that and offer you cash at the scene. You may see there is minimal damage and feel tempted to take the cash. No matter how insignificant the crash seems, you should always report the incident and see a doctor.
Damage to your car could be invisible
A minor fender bender may only produce a small dent or scratch on your rear bumper. It may not seem like much to repair, but there could be more damage hiding under the surface. Even a small fender bender can result in damage to the exhaust system or suspension. Taking a couple hundred dollars at the scene will not repair your exhaust, and since you did not acquire the other driver's insurance information, you are out of luck.
Injuries can remain hidden
You may also not feel the need to get your insurance company involved because you feel fine. This could easily be adrenaline blocking your pain receptors. Some people do not notice any symptoms or injuries until days or weeks after the crash.
Money for a rental car comes out of your pocket
Informing your insurance agency of the collision does not only lead to payment for car repairs. It can also pay for any time you have to take off work as well as payments to rent a vehicle. Your car may need to stay at a shop for a while, which means any rental car payments you need to make come out of your own pocket.