I think that while yes, it probably does happen somewhere at least once a day (i'm talking a long wait) the chances of it happening to you ...more than once....are slim. I think that splash mountain is the most likely to get "backed-up" probably due to how difficult it must be for someone with any type of physical disability to get in the log,but rides breaking down are not at all what stand out from my trips bc once you are off you just move on. haha. In all my disney trips there are only 2 times that vividly stand out in my mind that i was literally stuck on a ride. The first time i was probably 12 and a hurrican had passed over during the night so the parks were rainy and quite empty. we took this as a chance to go ride splash mountain over and over...until we got stuck literally right before the drop. great view but REALLY!!! haha finally we were evacuated..sounds like a bummer but it was actually a favorite memory of mine bc we got to walk around inside the ride!!! second "stuck" was honestly the scaredest i have ever been. i wont go into all the details but i am scarred for life where space moutain is concerned. i get so nervous i could cry in line...but i still ride it!haha
WOW...I can see how getting stuck on space mountain good be quite terrifying!