Here's a good discussion of stuff to do to stay safe while cycling. It says, among many other things (emphasis mine):
People wonder how riding bikes on sidewalks can be dangerous. First, there is a greater chance of minor collisions with cyclists and pedestrians due to poorer visibility and restricted room and also a greater chance of falling down. However, the likelihood of a collision with a motor vehicle also increases. These accidents occur at intersections and driveways, the former more deadly. Unwilling to dismount and often unwilling to wait for the light, the bike rider starts across the intersection parallel to the main road, completely hidden from a turning motorist until the last second, when it's often too late for the motorist to stop. A study of these risks was made in 1994 and showed that sidewalk cycling is almost twice as dangerous as cycling in the street, and cycling against the traffic on the sidewalk is over four times as dangerous as cycling in the street.
I can say that in 11,000 miles, the one time I was hit by a car was when I was riding on the sidewalk. Since then I've completely given up sidewalk riding.

That site also has a good discussion of how to avoid accidents.