Ok, now here's an interesting bit of research from Scientific American. A scientist who happens to be an avid cyclist ran an experiment where he attached ultrasonic sensors to his helmet and road around town, measuring how close the cars got to him.
Then he did the same experiment with nothing on his head. Then again, with a wig so that he looked like a woman from behind.
The result? Wear your helmet and the cars will get closer to you (which the article goes on to speculate therefore increases your chances of an accident). And if you're a woman, you'll get the most space.
I think that makes sense, although I appreciate the creativity of attempting to measure it. Without a helmet, I can imagine that there's something in the car driver's brain that sees "Hey, there's a person in the road." With a helmet, though, this "other people pattern recognition" is diminished and your brain processes it more along the lines of "Hey, there is another vehicle in the road." Not another car, but not a person, either. Then again your brain could just as well be saying "This person with the helmet is more protected from harm and thus it is safer for me to drive closer to him," but I'm not so sure about that one.
What he should have also measured was the distance granted him if he were just walking down the road (for instance, maybe pushing his bike). I bet that would gain even more respectful distance from the other drivers.