Buying driver's insurance if I don't own a car?

I grew up in NYC and then moved to San Francisco – two cities with excellent public transit – and so I have never owned a car. However, if I borrow friends’ cars, and I don’t have a car of my own (and hence no insurance), is that a problem, or would my friends’ insurance cover me from potential liability? Is it a good idea to buy driver’s insurance even though I don’t own my own car? I think it would also cover me for the times that I rented a car. Does anyone have experience with this, or know more about it? I am generally a very risk-averse person and it makes me nervous to drive knowing that I might not be fully covered. Also, if anyone has experience with this, how much does it cost to buy driver’s insurance for a non-car-owner?