I think Im right in saying the definitive appearance of this device was in one of the Indiana Jones movies (but please correct me if that isn’t the case); the hero just manages to squeeze through a door that is closing, then reaches back to retrieve his hat, but I’ve seen it referenced in a couple of subsequent movies and I suspect there are many more that I haven’t seen or noticed, so, let’s see if we can list them all; for starters:
Chicken Run - as Rocky and Ginger escape from the pie machine (Ginger’s hat)
Shrek 2 - as the ensemble escape from the potion room (Puss’ hat)