These are some examples I could think off but I don't think they are perfect:-
Conga Line(Dance):- Not perfect because people enter at the end of the circular queue but exit randomly. (People just leave randomly not in a serial fashion)
Airport Baggage Carousel:- Same reason as above. The baggages are picked by their owners at random.
Ferris Wheel:- Entry is in sequence, exit is in sequence as well. Once the ride is done, the position where exit starts from can be random (except the high roller in Las Vegas which lets everyone do exactly 1 rotation and is the one perfect example that I could find)