If you do not currently own a car and also do not have a car that you regularly drive you can purchase a Non-Owner / Operators policy. This will cover damages and injuries that you cause and are responsible for in the event of an accident. This coverage will not cover any damage to the vehicle that you are driving. If you are renting a car you will want to add their comprehensive and collision coverage that is offered in order to ensure the vehicle you are renting is protected. If you do not add the additional coverage then you will have to pay for the damages to the vehicle in the event of an accident, which can be costly.
If you are driving another person's car then you can still have a non-owner/ operators policy and the same coverage would apply as above. However, you do not qualify for a non-owner/ operator's policy if it is a vehicle in your household, and/ or it is a vehicle you drive on a regular basis. If either situation applies you will need to be added to the policy of the vehicle owner's policy as an additional driver.