Surprisingly, traffic signals have a longer history than turn signals as they date from the 1800's. The first traffic signal was installed in London by the House of Parliament in 1868. Since it was developed by a railway engineer, it resembled the signals used on railroads with semaphore flags for the day time and red and green lights for the night. The signal would pivot so that the correct ights would face the directions they were intended for. Shortly after it's installment, we had the first incident of traffic with the right of way having to slam on brakes for some jackass turning right on red.
The first electric traffic light was invented and installed in Salt Lake City in 1912. I'm not sure what it looked like. The first modern four way traffic signal was invented and installed in Detroit in 1920. I want to say it was installed on Woodward but I could be wrong.
The first interconnected traffic light was also installed in Salt Lake City in 1917. Six intersections could be controlled from a manual switch. Automatic lights came a little bit later.
Right turns on red are a little trickier. In Michigan they are permitted, provided traffic has cleared and there isn't a sign that otherwise prohibits it. So if there is a car in the right of way lane...do not turn right until it has cleared. Also, when you are coming up to a stop sign or light please do not gun towards the road.