I sold my car when I move to SF, and that was the best decision I made. If you have a rack and some good panniers or trailer to get groceries and other big stuff then you shouldn't have a problem. Everything in this city is biking distance, and almost always your bike will get you there faster than the bus. After a late night out at a concert or something it is nice to have your bike waiting for you so you can just jump on and get home in about 30 min, no matter where you are in the city. The late night bus can take almost an hour or more to get home depending on how long you wait (often that is about 20min+). Give me my bike any day. I won't even go into having a car and the BS that goes along with it, parking, shifting it around, tickets, and the list goes on.
A car might be nice for the occasional weekend away from the city, but it is hard to justify keeping it around for just those times. The great thing about the bay area is that you have opportunities to get out of the city with your bike. It's a short ride across the GG bridge, and once you get across you are in a great area for hiking, camping, and mountain biking. Point reyes is just about a 2.5 or 3 hour ride north to some great outdoor opportunities. Portola redwoods is about the same distance south. Take the BART to walnut creek and it's a short way to mount diablo. I could continue, but it might take all day to list all of the close beautiful places that are accessible by bike. Include caltrain into your trip and the list just gets longer.
I really do not think you will be missing your car. And if you start to panic or urgently need a car then maybe a car sharing program is right for you
http://www.citycarshare.org/