There was one instance at the county fair where the operator couldn't get the restraints open on one of the kiddie coasters, so they kept running it until one of the maintenance workers showed up. I must have ridden it 5 or 6 times in a row.
I was at Sea World San Diego, and Journey to Atlantis had broken down, but I wanted to ride it one last time before leaving, so I was in the first boat after they reopened it. After the first lift hill, the boat is supposed to slow down right before the large drop. That didn't happen. The brakes didn't activate and the boat coasted straight through. It wasn't enough to affect the drop, but it added some air time.
Then there was the time on It's a Small World in Disneyland when there were too many fat guys on one side of the boat, and instead of going around each curve gracefully, the boat rammed into one of the walls and got stuck, which then caused the boat behind us to hit us, and the boat behind that one to hit them. My father and some of the larger gentlemen had to get out of the boat onto where the animatronic figures are and push the boat until it started moving regularly again. It's not a small world, after all.