The quick answer is "It depends".
For some reason, I've been on a bike safety kick today, and I've done a little bit of reading. I've always been interested in whether it is more or less dangerous to ride my bike to work instead of driving. I know my wife worries about me also, especially in bad weather. One of the articles I read today can be found HERE. It has a very good description of some of the misleading statistics that are common today along with some well thought statistics on why bike commuting MAY be safter than driving.
Based on what I've read so far, if you are riding on the sidewalk, breaking traffic laws, and hugging the shoulder in heavy traffic, then YES... bike commuting is probably more dangerous than driving. If you are using the road like your supposed to (like a VEHICLE), obeying all the traffic laws, and "taking the lane" when in heavy traffic on narrow lanes, then you are probably (in my opinion) safer on a bike or at least close to as safe as driving. The downside to riding like your supposed to, is rude drivers that have to go AROUND you instead of buzzing you with inches to spare. Your likely to get a few more honks from the folks that are running late for work because they stopped at Burger King to get an "Enormous Omelet Sandwich". But heck, your saving money and getting some great exercise.
So stay off the sidewalk, use flashing front/rear lights, pretend your a car, obey the traffic laws, ignore the rude drivers, and your golden. Oh, and wear a helmet, preferably a green one. ;-)