papaver -- are you Dutch perchance?
Having just read Bob Mionske's Bicycling and the Law it is pervasive in the US that you're lucky as a cyclist to be recognized as having any right to the road. Around here, we have a cyclist who is doing his part by recording and reporting unsafe driver behavior (
http://bikesafer.blogspot.com/ ). Sometimes he has success; sometimes his interactions with the officers sworn to protect us just makes you want to cry.
But, yes, I'd probably say that at least once a week a car passes too close (and my state does have a 3 foot law), scoots in front of me to turn, or shouts things at me. Only once have I been intentionally run off the road and feared for my life.
You need to ride defensively. Assume you're invisible. Take the lane if it isn't safe for the driver to pass and assume every driver of every car is an (explicative deleted) until proven polite.