My entry for the official MindStorms forums' 9th Community Contest
The actual lifting mechanism (the big box on top) is just a box of bricks, the gearbox and a wheel. I noticed that the large (thick, not wide) Lego MindStorms wheels all have a very small hole in them. I threaded some fishing line through that hole and tied it in place, so that when the wheel was rotated, it would pull on the cable and wrap it around the wheel. The fishing line was then passed through a 2x1 beam's hole to guide it so that it would wrap around the wheel and not the axle holding it in place. The wheel was built into a gearbox (constructed from three 8 tooth gears and three 40 tooth gears) and the motor was connected to the gearbox input. I don't know how to calculate the gear ratio but there is a fairly large torque and speed difference between the input and the output. At the end of the fishing line, there is a plastic bag, secured to the line by looping the line through itself and inserting a thin plate into the loop.