I've never seen anyone removed from a flight.
One time I was on a flight from Detroit to Atlanta. The plane had just taken off and the seat belt sign was still on. An older gentleman a few aisles back decided that he couldn't wait any longer and got up to go to the bathroom. I didn't see him get up; all of a sudden there was a stern "Sit down now!!" over the intercom from one of the flight attendants.
Another time flying to Atlanta someone on the plane was ill -- not violently throwing-up ill but it almost seemed like they were having a seizure of some kind. The flight attendants found a doctor or nurse to check the person out and a decision was made to request an emergency landing. We were close enough to Atlanta that we weren't deverted, but (a) we apparently were put to the front of the line, and (b) we made the fastest descent I've ever experienced on a commercial airliner.