Some insurance companies require a police report in order to file a hit and run under uninsured motorist coverage.
I had someone run me into a median curb one time. I tried waving down several witnesses but they just drove off when the light turned green. I didn't think the damage was that bad, but it turns out that I busted the oil pan. Since I didn't file a police report, the insurance company forced me to pay my deductible and filed it under comprehensive coverage. Note that this was only because I avoided being hit by the other vehicle - it would have been covered under uninsured motorist coverage if I had let them hit me. Now I know
I call police first and my insurance company second at the scene of any accident now, regardless of how minor. I've even had my insurance company take a statement from the person at fault on my phone at the scene. They later tried to change their story, so I was glad the insurance had already taken their statement admitting fault.