I agree that car accidents still happen. But honestly most my near misses with cars were outright insane.
One in particular gives me chills. I was driving along an empty road and a car wanted to make a right-hand turn onto the road. The car driver came to a stop at the side road, we were close and it was clear enough that I made eye contact with the middle-aged woman driver. I swear she looked me right in the eyes, then she proceeded to drive right out in front of me. I swerved, slammed on the brakes and slid up next to her car (luckily there was room on a single lane road). She just waved at me apologetically. I wore a bright red and white (with reflective strips) jacket, bright green and white pants, black and white reflective helmet and my motorcycle was bright green, it was the middle of the day (but not glary) and I had my headlights on regardless.
I'm absolutely convinced she saw me, we looked right at each other, she was just in a bit of a daze and a motorbike didn't register as a car, so she just pulled out. Now, it's true she could have done the same with a car. Obviously, I can't know for sure, but I absolutely believe if bikes were more common that situation just wouldn't have happened - at least, not like it did.
EDIT: To clarify, I'm actually in Australia. So for you US folk it was a left-hand turn she was making ;)