I consider myself to be a "core" gamer, by which I mean that I would rather shoot things than farm things. I don't, however, consider myself to be a "hardcore" gamer, which means that my difficulty setting of choice has always been "Normal." I've never had a whole lot to prove in the skill department, and Xbox Achievements are not actually a huge draw here, contrary to my long, torrid history with them.
Despite all of this, some games have gotten me to change my difficulty, and I've isolated a few reasons why.
1.) New content
This feature is exceedingly rare in the game world, but some titles have incentivized replay by locking additional plot or character details behind the higher settings. This is kind of a sneaky trick, but it worked on me, so it is what it is.
Developer Remedy Entertainment's 2010 thriller Alan Wake, for example, had some of its collectible manuscript pages (that revealed more information about what was going on) only available on its most difficult setting. I'm a huge fan of knowing what's going on, so I replayed the game and collected every one of them. I only regretted it until I devised a method of running backwards and flashing my light at enemies to slow them down until I could make it to a safe haven, which probably looked ridiculous to anyone watching, but you can't argue with results.
2.) Let me keep improving
The biggest obstacle to me playing on "Hard" is the difficulty. That's pretty obvious, but when I'm playing a game, I expect to enjoy myself. Dying 15 times in a row in the same room is not really my idea of fun. It helps, though, if I can carry my inventory from previous playthroughs along to the new run, especially if I can continue improving them.
The grinds in Max Payne 3 are slightly related; they do not reset when you start a new game. They are certain tasks you can perform while playing (e.g. "Kill X guys with shotguns"), and your progress carries over. I'm currently replaying Max Payne 3 on Hard just to work on my grinds. Granted, I am doing this for Achievements, but I like the game enough that I don't mind dying all the time (which I do).
3.) Smart challenge
The easiest way to increase difficulty is either to make enemies do more damage or make the player do less. Batman: Arkham City sidesteps this entirely, offering a New Game Plus mode that is essentially a remix of the regular playthrough. Enemies appear in different places and in new configurations, and the "Spidey-Sense" visual cues to counter do not appear at all. Arkham City's challenge mode is exactly that: challenging. It isn't cheap; if you were paying attention and really trying to be good at combat the first time around, you already know everything you need to know to get through it.
The boss fight with Mr. Freeze (one of my favorite boss fights of all time) is actually improved in New Game Plus, as each of your tactics does less damage, requiring you to pull out almost every move at your disposal to win. This encounter serves to crystallize the versatility of Batman's arsenal in this game, and it really puts the sheer number of tactics at your disposal into perspective.
4.) New weapons
I played the hell out of Silent Hill: Homecoming, and I'm pretty sure I'm the only one who did. As soon as I finished it, I started a new game because I knew that I had a badass Laser Pistol somewhere in my near future. That knowledge alone was enough to make me ramp up the difficulty, because I was so excited about shooting monsters with a laser from space.
The Laser Pistol actually breaks the game, difficulty-wise. It has infinite ammo and can even kill most bosses in just a few hits. I'd already beaten those bosses once, though, so I figured I'd earned my little ray gun.
So, to recap, here are the things that'll get me to play on Hard:
An opportunity to build upon my existing skills
Not just the same game, only harder
What do you like in a Hard mode? Let us know in the comments.