I live by a traffic circle (we call em roataries up here in Boston). A couple of years back, I was taking the bus to work for a while; so I was sitting on a bench across the street in the morning during rush hour. It was quite a sight.
The key isn't to watch it while its moving, its to watch what happens when it stops. A pedestrian walks up, hits the button, and the lights turn red....and within seconds there are stopped cars everywhere. The whole road is bumper to bumper.
Then another pedestrian walks up, looks at the light, stops, then suddenly decides to cross now as it changes back to green, and for another few seconds it stays as it is.... within about 10 seconds, the traffic is moving again and all the input roads drain off. It is impressive to watch.
Also, I note people seem to think rotaries are dangerous, and I can see why, as cars mill around, weaving in and out, you have to pay attention, everything works out fine, but it forces you to pay attention and actually think about how to merge properly. Most people end up playing it conservatively and waiting for traffic to stop.
Thing is you might think that takes a long time, but it never does. Because every car that turns a different way blocks off incoming traffic from one direction, opening it for another. Just the random pathing of cars exiting the rotary is enough to keep all sides flowing generally...and even when it doesn't, its not too terrible, the circling paths open up opportunities to merge often enough. I watch this happen every day as I go through about 4 rotaries on my way in to work every day. They really work.