The CM's definitely do move strollers at some of the rides. I would bring a bright bandanna or something to tie onto your stroller so you can find it when exiting rides. In January, the stroller parking lot in Fantasyland in MK became unbearable. There had to have been well over 100 strollers parked outside of some of the rides. It left a path about 10 feet across to walk thru. This was in the afternoon. We usually hit Fantasyland first thing in the morning because it can become almost impassable in the afternoon. Don't leave anything of great value in your stroller while on a ride. We haven't noticed anything missing, but have found our possesions sorted thru when we got done w/ a ride. I assumed it was just some child that mistook our stroller for his own. The Disney rental strollers are hard to tell apart, so do mark your stroller w/ something so it is easy to spot.