I usually use Easy or Normal modes because I want to play it without trouble, and the exception is when I play Black 2 that I choose Hard mode, because sometimes Hard mode gives rewarding features or more in-game moneys.
Normally I play a game for the story and for the multiplayer. Some game, like the Batman games, I play to know everything and try to get all of the achievements. Most games though, I don't explore every nook and cranny because it won't interest me as much. Staying at a lower level is fine with me, I normally play most games at the "Normal" difficulty because I don't want to stress out playing on a higher level.
I always play my games at the lowest difficultly level, except for Star Wars: Shadows of the Empire, where I have played all the way to 'Jedi'-the highest difficulty level available.
Most other games I couldn't do the higher levels at all anyway, so...
I play most games on the second to hardest mode. "advanced" mode I guess. There are some games which there are only 3 difficulties, in which case I usually go around once on Normal and again on Hard, alternating depending on how easy/difficult they start getting.