I was driving today and making a right hand turn at an intersection. Just as I am approaching the apex, a wrongway cyclist, that is also turning left, is coming right at me. I startled a little and had to alter my line and go to the outside in order to leave him room. He was going fairly fast and seemed to know what he was doing (in the sense that he was a fairly smooth rider, but he was clueless in riding the wrong way) in that he didn't panic, but if I hadn't altered my line, he would have bounced off the side of my car.
Not that it needs repeating, but people just aren't looking for someone riding a bicycle the wrong way.