Raiding other players treasure dens.

[Opus]

Or maybe people just can't stand stuff lying around and feel the need to clean up the mud.

I belong to that category of people.

[Carrion]

The next question is: What do you hide in your stash and why?

You're really in the zone, Opus

1) Quest items that are stashable (obviously not storable), and not easy to get, AND when the quest is somewhat hard to finish in one go
2) Things not storable but good to have right away when entering but not really hard to get (typical example is a backpack)

Third example would be to share equipment between chars, but I actually don't think I ever do that...

Of the above, the quest items seems to be the "bad" part, but I honestly try to finish the quest as fast as possible when I have such items stashed...

[Escaflowne]

I've been trying to solve something lately that relieves on a 'stashed' key.

You mean that the key is unique?  That's just bad coding.