I recently encountered a situation where the car in front of me did not have any functioning brake lights. Unfortunately, I didn't get the license plate number, but in the future, how should this be reported? The only thing I could find online was something on answers.com, but I don't exactly take such a site as gospel truth and am looking for further information here.
It is illegal to operate a vehicle on public roads without functioning brake lights. So if you observe such a vehicle "the system" for addressing it is to call 911 and report it. If available, police may try to find and stop the vehicle. At the discretion of the responding officer the vehicle operator may be given assistance, a warning, a citation, or may even have the vehicle impounded on the spot. The officer can also use the stop as a pretext to further detain and harass the operator.
(As noted in the comments, this "system" can be disturbingly unsympathetic in addressing such problems. One might consider "the neighborly thing" to be, if possible, to alert the vehicle's operator to the problem, and encourage or help them to fix the hazard.)
Call 911 (in the USA, atleast). That is actually a very dangerous situation. Don't worry about the driver getting harassed by police. If they were riding dirty they would not have broken tail lights.