There are many ways games can "up their difficulty." The most used, I think, is weighting one side or the other over the the other. This can be include weapons, armor ratings, health, and other "combat" factors. But games can be about more than just combat. Even in that arena, AI is rarely made more difficult so that strategy plays a bigger part.
I've been playing a lot of NCAA Football and have come to find one of their "difficulties" very enjoyable. No, It's not an RPG or set in a fantasy setting. But it has a difficulty based on something entirely different.
A little explanation of the game, so skip this next paragraph if not interested in American Football
In college, a big portion of the program is recruiting high school football players and entice them to come to your school. This is the part I enjoy most in this game. How they do this is there is a list of what your school has to offer each new player and the game gives each school a rating, or grade, from A+ to D- (lowest I've seen so far). There are also some aspects that change every week, like "playing time" or "playing style."
OK, are you back with me now? The "difficulty" comes in here via large school vs small school. My first foray into the game, I chose my favorite collegiate team to coach: Michigan. It is a top tier school with good facilities, a good reputation, and many players enter the professional league. I had 3rd string players that could have started for some of the other teams.
My second foray into the game, I took Wyoming, my favorite state in the U.S. The differences in difficulty I encountered astounded me. Barely anything I had to offer incoming players was rated "D" or higher. I no longer could focus on the top prospects (4 or 5 star - how players are rated) Like I did at Michigan, but had to go after 1, 2, or 3 star prospects.
The difficulty comes in trying to build a successful program vs maintaining a successful one. It's a much slower process taken in baby steps. This also trickles down to the actual gameplay. I don't have the "star players" like the big schools do. My depth chart, or back-up players are rather poor players. There is a huge gap between my starters and their back-ups. An injury to one of my starters can be devastating. The games are much more difficult, do to the gap between player talent. This, in turn, feeds back into the recruiting process, as winning is a struggle until I can recruit a few of the better players.
This is possible, though. I may get a local talent that doesn't want to be far from home. I may get a better prospect from a state where I have a bunch of players already (called a pipeline state) and have those current players help influence the new recruit. And no difficulty slider is even needed
tl/dr:
Bunch of stuff about an American Football game and one way difficulty is handled.
Since I have a feeling not many posters here play NCAA Football (or any sports game), let's get this to something where others can participate.
What kinds of difficulty do you seek when you play? Is more health/less damage enough for you? Would you like to see better AI?
In Skyrim's case, I know many players like the mod that makes Dragons actually scary. There are also other mods that make enemies with better AI. Is that more of the experience you're seeking?
I know a lot of players love combat, and sometimes just weighting the health/damage is enough, as it makes combat take longer. Are you in this camp?