It depends on their insurance. You will only be able to drive their car if you are either a named driver on their policy or their policy is for any driver. The latter is unusual as it is very expensive.
In the UK it is the car that is insured not the person (as in the US I think) the policy for the car must therefore specifically cover you as a driver.
I'm posting here, however, to correct Hamish's post. Cars don't require insurance. Drivers do. For example, if my friend lets his insurance policy expire, I can still drive his car (because of the 'third party - any vehicle' provisions in my insurance). The fact that the policy which specifically referred to that vehicle has run out is completely irrelevant.