I've only recently begun playing games in other difficulty settings than Normal and usually I need to get a trophy to be arsed to do it. I guess it's mostly because I have so many unplayed games in my collection that I don't really have the time to play all of them on Hard or Impossible or even harder.
My list is as follows:
Call of Duty: Modern Warfare 2 (Main Story: Hard, Veteran; Spec Ops: Hard, Veteran)
Dead Space (One Gun)
Dead Space 2 (One Gun, Hard, Impossible; Hardcore until the last three chapters)
inFamous
inFamous 2
Mirror's Edge (No weapons used)
Uncharted: Drake's Fortune (Hard, Crushed)
Uncharted 2: Among Thieves (Hard, Crushed)
Elite Beat Agents (Cruisin', Sweatin', Hard ROCK!)
There might be some I've forgotten.