On occasion. Depends on the game really.
I have no intention of playing something like Oblivion, Fallout, or even ME2 on the highest settings (especially since ME2 on Insanity isn't challenging; it's just fucking annoying). Most action games however, I may bump up the difficulty (i.e. Ninja Gaiden Black or Bayonetta) if I feel that the easier difficulties are literally no fun.
Take the Dragon Age games. I'm having quite the blast playing on the easiest difficulties (also because I have no real concept of tactical management; I'm more of a "feeler" than a "thinker" in that regard). Action-esque games like Vanquish or Ninja Gaiden 2 I actually have to cut the difficulty up because the games became so easy they weren't any fun.
Although, on easier difficulties it's easier to get your own "A God Am I [http://tvtropes.org/pmwiki/pmwiki.php/Main/AGodAmI]" kinda vibe when you lay waste to everything with nary a blink.