Insurance company claim guidelines differ however yes, normally if you have been in an accident you can file an auto insurance claim without a police report however it is recommended to obtain a police report if possible. Insurance companies will use the information on the report to help determine fault, understand where the accident took place, see the responses by both parties.
The police report can also be helpful to those involved in the accident, especially the not at fault party who can get the at-fault party's insurance information, name, license plate number, etc from the report.
In most instance though an insurer will accept a claim without a police report, especially if you contacted the police and either they were too busy to come to the scene of the accident, and thus request that the parties involved exchange information on their own, or will not take a report for some reason. There are some that decide to not take reports on private property.
If you have been in a hit and run accident though most insurance companies will require a police report and with this type of accident if you have any independent witnesses that viewed the person hit your vehicle and flee it can help with filing your claim.