Which aircraft have elevators (lifts)? How do they work?
After researching myself and asking a colleauge I found out that the L-1011(one of my favorites) 


and the DC-10 (thanks to @UnrecognizedFallingObject for the comment)


had persons elevator.

On the Tristar and the DC-10
The purpose are to connect the Main Deck with the personnel-cabin or the Lounge.
.

The Mechanism as "@ratchet freak" stated in the comment is an "rack and pinion gears" elevator with 1 electric motor with 1 outer shaft (primary) and 1 inner shaft, as stated in an report of an incident with one of these elevators.

On the A380 there is an elevator to connect the 2 main decks, but this one is only for trolleys.



Edit:

Additional Information on mechanism of elevator:


  Drive System
  
  Each lift is operated by an independent drive unit. Each drive 400-cycle, three-phase, 
  alternating current (AC) motors. Each motor is connected to a gearbox with 
  counter-rotating drive shafts and sprockets for a chain drive. The drive shafts are 
  operated by a common worm gear within the gearbox. In the
  event of one motor failure, the other motor will drive the lift at
  half-speed. Two, independent, continuous loop, bicycle-type chains taking power from the
  dual-output sprockets on the drive units actively drive each lift.
  
  
  
  Limit Switches 
  
  The range of travel of the lifts is controlled by limit switches installed
  within the wire duct attached to the forward side of one of the vertical lift
  tracks. There are two sets of two limit switches for each lift:
  one set located in the service center and one set in the lower galley.
  One switch is a normal stop switch and the other limit switch is for
  overtravel in the event the normal switch fails to operate. 
  The limit switches are actuated by a cam plate mounted on the side of the lift.
  The cam plate has a machined offset to prevent actuation of the
  overtravel limit switch unless the normal switch fails to operate. In
  addition to the limit switches, mechanical stops are installed in the
  vertical lift tracks to stall and shut off the gear motors if both
  limit switches malfunction.
  


Further and detailed Information can be found here in this Incident.