I have to cross a lot of rail tracks on my commute, which requires a fair amount of planning and focus on a skinny-slicks road bike. My only real bad accident was getting cut-off by a cab pulling over to pick up a fare, right as I was nearing the rail tracks. Instead of acellerating and hopping them at a proper angle like planned, I was forced to brake and swerve to avoid the cab, causing my front tire to drop right into the track, snapping me over sideways onto the ground pretty hard. That was one of the main reasons I decided to get a dedicated commuter bike with fatter treaded tires, instead of taking my road bike to work. I have a lot more room for error when crossing tracks now with the 40c tires on my commuter bike.

I've also had a ton of close calls with cars turning right without signaling, right in front of me... luckily haven't actually ran into one yet. Some were VERY close calls, though...