Who is at fault if a car is parked at the edge of a driveway and a car from the driveway backs into the parked car?

The person backing up can be held accountable, since he is responsible for knowing what is in his line of backing. However, you can also be held responsible for blocking his driveway, this is considered a safety hazard. Most city ordinances have laws against parking on sidewalks and blocking private entranceways and driveways. So, you both could be in trouble but the car blocking the driveway will be cited with stiffer fines.

Note that most states have some form of comparative negligence in analyzing cases like this. It is likely that the vehicle blocking the driveway would be assigned some level of negligence for blocking the driveway. However, it is probable that the majority (if not all) of the negligence would be assigned to the person backing out of the driveway, because his vehicle was in motion and he is supposed to be aware of its direction and speed of travel and any potential hazards it may encounter in its path. If I had to make a guess, negligence might be assigned 90/10 or 80/20. Depending on the jurisdictions form of comparative negligence, any damages would be split accordingly.