The smoothness with which air traffic is usually managed means that, whenever something doesn’t go to plan, it is quite a surprise. A go around on approach is a relatively rare occurrence. I have only been on three commercial flights that spring to mind when a go around was executed. I saw a couple at SFO last year on one day but that was when two of the runways were shut and they were squeezing as much as they could in making the chance of a conflict higher.
I was watching arrivals to Chicago Midway when I saw a Falcon 2000 on approach. As they got closer, they obviously got the call and the aircraft pitched up and applied power to climb away. It made for an unusual angle at which to see the plane as it banked away on to the missed approach procedure. It obviously was not a complicated procedure because they showed up again shortly afterwards. They were then followed by a similar Falcon 2000 and it was only later, when I was going through the pictures, that I worked out which one was the jet that had made the go around.