I travel by air a lot, and at virtually every airport I've ever been too, including where you disembark by stairs, as opposed to by jet bridge, the left-hand-doors are always used; and the right-hand-doors are used for loading catering trolleys, etc. I understand why it would be useful to standardise this within a particular airport, but not between different airports. Is there any good reason for this? Conjecture is OK, but a verifiable answer would be best! :)
Nate is correct, because the Galley is loaded from the right (and on a 737 is on the right hand side (centre for bigger planes)
Page 6 of the this PDF shows Boeing 747 design specs and how a plane is serviced while on the ground under normal circumstances. You'll notice that the cargo is also loaded on the right hand therefore if a plane was being unloaded via stairs it would create a substantial hazard.
The "left" side of the plane is usually referred to as the Port side. The term most likely comes from terminology as used for Ships (Fore, Aft, Port, Starboard, Up and Down). I would say it is convention that ships dock such that the Port is on the left, from which the term for the side gets its name ("The side of where the Port is").
I expect it's because most airplanes are designed for boarding and deplaning on the left.
Next time you're on an airplane, take a look around as you're boarding. In my experience, the area around the boarding door on the left is relatively spacious and designed to direct passengers into the cabin. The corresponding space on the right is usually a galley. It would be less convenient for passengers to have to pass through the galley to board or deplane, and would interfere with the ability of crew to work in the galley (preparing drinks for oncoming passengers, or cleaning up after a flight).