It's a Small World Breakdown: On November 27, 2009, It’s a Small World broke down while a guest with quadriplegia was on the ride. The guest was stuck in the "Goodbye Room," unable to leave and forced to listen to the horrific earworm of the ride’s theme song for 30-40 minutes before he was finally evacuated. He sued Disney for not having adequate evacuation procedures for disabled guests, and in March 2013, he was awarded $8,000.
Seriously though I am surprised deaths don't happen more often. The Walt Disney parks had 132,549,000 visitors just in 2013. So just in that year alone the average was more than 37 thousand people per day.
I'll bet you it is statistically safer to play and have fun inside their parks than the trip flying or driving there.