Hardcore - absolutely my favorite. I play this mode most of the time.
Cursed - I've tried this a few times and tried hard to like this mode, but I just don't.
Ego - Good for people who consistently play at dungeon levels higher than their characters, but for more conservative players, getting half xp most of the time is frustrating.
Unlucky is a nice option, but I prefer modding the item code to customize the quantity and quality of drops to my liking.
Poverty - Tried this a few times, but with not that much to spend money on, characters often still generate more than enough cash.
Semi-hardcore - death makes the character weaker and weaker until the ultimate death. Haven't tried it but seems frustrating. I would have preferred a system where you start with one life then gain an additional life (kind of a Din's blessing thing) say every x levels, or one or more lives with each gain in status (freedom, champion, elite, etc).
Hunger - Haven't tried this, but I have played enough roguelikes to know what it's like. There, foods are often hard to find, and staying well nourished can be very difficult. Since foods are readily available in Din's, I can't see this being much of a challenge.
Lost - I've tried this a couple of times, and again I think roguelike experience helps here. If you "wall hug" and move around in one direction you should do ok.