Does car insurance cover rental cars?

Comprehensive and collision coverage extends to rental cars, while liability insurance does not. You should check your policy to see if coverage applies to rental vehicles and, if so, what stipulations or limitations there may be.
If your policy does not offer rental car coverage, you may have some limited coverage from your credit card; you can purchase insurance from the rental car company; or you can shop for a standalone rental car policy (that is typically cheaper than what the rental company will offer).