When an intersection has stop signs, the right-of-way depends on whether the stops signs are on all four corners or just two. If all four corners have signs, then the first to arrive and yield to the right rules apply. Otherwise, the road with a stop sign must yield to the party on the road without the stop sign.
When an accident occurs away from an intersection, the right-of-way varies. For instance, a driver who exits a private driveway must yield to oncoming traffic. In many states, failure to yield when exiting from a private drive is negligence per se. Liability varies for accidents that occur mid-street. They are fact specific. Also, many states bar recovery from anyone who had the last clear chance to avoid the accident. If you have been involved in a bicycle accident, contact your local personal injury attorney to find out what rules apply to you.