A paternoster is an elevator that moves in a continuous loop, never stopping. It moves more slowly than regular elevators and people simply get on and off when they need to. Dating back to 1884 and most common in continental Europe, the paternoster has become a bit of a dinosaur due to safety concerns. (For an excellent visual of how the paternoster loops up and down, visit this Wikipedia article).
This one is in the Attenborough Tower of the University of Leicester, UK.