It all depends on the game, the genre, and what kind of feeling I am trying to get from the game. One rule I have though is I almost never start off on the hardest difficulty. This is so that I have a good reason for playing through again besides just enjoying the story once more (and also so that there is continued challenge escalation on further playthroughs now that I know what to expect out of the game.)
If I've already been playing other games in the same genre, I'll aim for harder rather than easier difficulties, but at the same time if it is a new genre or one I am out of practice with, I may choose an easier setting. If the controls seem particularly intuitive and I grasp them quickly I will then occasionally restart on a harder mode before I have even finished the game.
Most recent example is ODST. I played through all of the Halo games leading up to it (heh, backwards, ending on 1, so that I would be fully prepared for the return of Health and Pistol.) I started off on Heroic from the beginning and was not disappointed with my experience. Enough of a challenge to make me feel vulnerable and squishy, but easy enough that I could work my way out of the hardest parts before getting frustrated (my frustration seems to escalate faster with games than with every other experience in life combined, unfortunately, and it can ruin a game for me.) I now very much look forward to the Legendary experience.
If I've already been playing other games in the same genre, I'll aim for harder rather than easier difficulties, but at the same time if it is a new genre or one I am out of practice with, I may choose an easier setting. If the controls seem particularly intuitive and I grasp them quickly I will then occasionally restart on a harder mode before I have even finished the game.
Most recent example is ODST. I played through all of the Halo games leading up to it (heh, backwards, ending on 1, so that I would be fully prepared for the return of Health and Pistol.) I started off on Heroic from the beginning and was not disappointed with my experience. Enough of a challenge to make me feel vulnerable and squishy, but easy enough that I could work my way out of the hardest parts before getting frustrated (my frustration seems to escalate faster with games than with every other experience in life combined, unfortunately, and it can ruin a game for me.) I now very much look forward to the Legendary experience.