Even though cyclists often receive the brunt of the injuries that occur during car-bicycle accidents, the fact is that a cyclist can actually be found primarily liable for his injuries--and the injuries of a motorist--should they end up in court.
Because, just like motorists, cyclists must obey traffic laws, and a failure to do so is strong evidence of negligence, and thus fault.
As with all injuries, bicycle accident liability comes down to which party was negligent, and whether the parties contributed to their own injuries.
Beyond the usual considerations of whether both the cyclist and motorist were acting with vigilance, negligence in bicycle accidents essentially boils down to whether one or both parties failed to obey traffic laws.
Whatever your opinion, the fact is that, in most states, cyclists must obey traffic laws. This includes following the flow of traffic, obeying traffic signs and signals, observing basic rules regarding turns and lane changes, and following drunk "driving" laws.
A cyclist hit by a car after he blew through a stop sign is likely responsible for his own injuries and that of the motorist. Same goes for bicycle accidents caused by cyclists failing to make hand signals when changing lanes.
This, however, doesn't mean that cyclists are always primarily liable for bicycle accidents in which they were negligent. Motorists are expected to respect the place of cyclists on the roads, and disregarding their presence and safety is just as negligent as not obeying traffic laws.
Indeed, the only way to prevent liability for bicycle accidents is to follow the rules of the road.