All biking accidents that I've heard of involve cars.
In the city, the most dangerous things are driving next to parked cars (people open doors without looking) and crowded intersections (cars turn without looking).
On the country side, the most dangerous thing are cars passing cyclists without sufficient distance. Drivers are really bad at estimating the distance of their side mirror to cyclists.
Anyway, that's anectotal evidence from the handful of serious accidents that people I know had. Personally I've been lucky so far.