What are the most difficult, yet rewarding games you have played?

Some games seem to be hard just for the sake of being hard, and as a result the difficulty feels unnecessary and overdone. For example, Skyrim on the highest difficulty just makes enemies do more damage, and makes you do less.  On the other hand, there are games like Dark Souls, which are seriously difficult but also fair. Once you learn the enemy's movements and attack patterns, generally you can defeat them somewhat easily.

What are some other games you all have played that fit this category? I would love a new game that makes me feel like a complete newbie again.