I prefer games that other people think are really hard, but hard in a way that requires thought rather than twitch skills; Super Meat Boy is really hard, but not my style, for instance, that's a lot of muscle memory/reflex skill. I prefer ... "intellectual" difficulty? That's a bad word and not really what I mean, but I think it conveys the point. I love puzzle games, the harder the better.

I like Dark Souls, because it's pretty hard but the skills that it requires aren't really twitchy and reflexive, because it's not fast-paced despite being an action game.

I really love hard turn-based games the most. I feel like I mention the game a lot, but Divinity: Original Sin on Tactician difficulty? Sign me up.

I really hate difficulty that is just a test of patience as Psy said - how long can you repeat this single pattern to wear down a giant HP sponge, for instance.

On the "easier" side, one thing I've always appreciated about Dragon Quest is how balanced the games always feel, all the way through - I never feel like I have to grind (well, except for in DQ1 or whatever of course, which is really a kind of different style than the rest in reality), but I never feel "too strong" for the areas I'm in either.