I've been stuck on plenty of rides. Usually for Indy. Most memorable was one time on Indy where we got stuck about halfway through the ride. It started up again and went a bit further, but eventually the lights came on. After sometime, CMs came and let us off and we walked from Jeep to Jeep through the rest of the ride, helping other riders get off. It was pretty cool to see the place with the lights on.
I've also broken down twice on Space Mountain, but both times were not IN the actual ride. Instead of turning right to enter the ride, we turned to the left and were required to evacuate our car. Once the entire ride was broken when this happened, the other time just the car we were in failed.