Yes, you can drive someone else's car without having your own insurance policy. In this case, the car owner's insurance policy usually comes into play. As long as you have the owner's permission to drive, their insurance should cover you. It's like the car carries its protection no matter who is driving.
However, if the car owner doesn't have insurance or if their policy doesn't extend to other drivers, you could be at risk. And if you regularly borrow a car, you may need non-owner car insurance.