We have lived in the South Bay for 2 years and are now moving to the East Bay. We had a car initially, but when it died, we didn't bother replacing it. So far we've been fine, we might get one if we have a kid.
One thing to be aware of is that there are multiple public transit systems in the area that don't necessarily have a lot of overlap. For example, your office might have great access to BART but that really only runs north-south through SF (and then branches out in the east bay), so if you live somewhere like Outer Sunset you could be looking at a bus/light rail + BART commute. There are a lot of cyclists though, and the weather is good for cycling a large chunk of the year, so if you both live and work in SF proper, you may be able to skip public transit entirely.
In a lot of areas, parking a car is also a PITA. In any of the really urban areas (SF, Oakland), you'll probably pay extra for an apartment with offstreet parking, and if you park on the street, make sure to pay attention to the local street cleaning schedule (this could be a difficult thing to keep track of if you don't actually drive regularly).
