I've been on rides when they stopped briefly at WDW, but never evacuated. On the other hand, I've evacuated off 3 different rides at Universal - Cat in the Hat, The Mummy, & Jurasic River Adventure. (The River Adventure one really sucked. We were stuck in the boat right before the drop for 45 minutes. They finally got us off of it & we had a 5-6 flights of stairs to climb down.)
I also got stuck at Cat in the Hat. I was so looking forward to riding too since Dr. Seuss land was so cute . We waited for a bit and saw people jumping the line to get out so we just followed. We had free tickets with our hotel room rate and were only there to see Harry Potter, so it was not that big of a deal. HP broke down multiple times while waiting in line and we ended up waiting 1.5 hours, but it was an awesome queue and well worth it in the end. Amazingly enough, Cat in the Hat was still broken hours later.