Easy games can be really fun, but I think most gamer's enjoy a challenge. Now this challenge can either be frustrating or rewarding, possibly both.
What are your favorite games that are difficult but did not discourage you?
Here are some of mine...
1.) Bungie Games "Myth Series, Halo"
I never feel like I have truly completed a Bungie game until I have completed it on the infamous LEGENDARY difficulty level. No matter how hard the games get at points, I always keep trying until I complete it. On Myth, I used to love to play Cooperative mode online on Legendary and try to beat a level without losing any units. The Halo series is the same for me. Either solo or cooperative, it is a true sense of accomplishment once you beat the game on Legendary.
2.) Mike Tyson's Punch-Out
The sense of being able to do a perfect run on this game is what I like about it. While most of the characters aren't that difficult, Mike Tyson is a pain until you've played the game a ton. I enjoy playing through this one over and over.
These are 2 examples that give me the feeling of accomplishment, as opposed to discouragement/frustration, that I am trying to describe.