The legal duties every state imposes on a driver involved in a crash - to stop, to exchange information and to help anyone hurt - and the separate criminal offence of driving away instead.
A driver involved in a collision - with another vehicle, a pedestrian, a cyclist, or unattended property - is required by every state to stop at or near the scene, to give their name, address, vehicle registration and (on request) licence and insurance details to the other party or the police, and to render reasonable assistance to anyone injured, which at minimum means summoning help. Where the other party is not present, as with a parked car, the duty is typically to leave a note and report the collision. Fault is irrelevant to these duties: a driver who did nothing wrong in the collision commits the offence by leaving.
Leaving the scene is a criminal offence in its own right, separate from any charge arising from the crash itself. Its grade depends on the harm: leaving after property damage is generally a lesser offence, while leaving after an injury or death is a serious crime in every state, often a felony, and frequently punished more heavily than the underlying crash would have been. A conviction also brings licence consequences and, for insurance purposes, may allow an insurer to deny coverage.
The offence requires knowledge - that a collision occurred, or that it was reasonably apparent. A driver who genuinely did not know they had struck something is not guilty of leaving, though what a driver "should have known" is often the contested question, and returning to the scene or reporting promptly matters both to the charge and to how it is treated.
If you have left a scene, even a minor one, the sequence in which you report, speak to police and speak to your insurer matters, and it is one of the situations in which talking to a lawyer first is the practical course rather than the evasive one. If you were the person hit, an uninsured-motorist claim on your own policy is often the route to compensation when the other driver is never found.
Choose your state. Each link opens the directory page for the city in that state with the most currently published law firms in this practice area; a +n beside the city is how many other cities in the state also have one. The list is generated when this page loads, so a state whose listings have lapsed drops out rather than becoming a dead link.