I like a game that is just hard enough to only mildly frustrate me. That way I'm still having fun and I feel like I'm actually demonstrating some level of skill.
Dead Rising, for example, maintained a pretty standard difficulty throughout the game - as long as you minded your surroundings, you'd be more or less fine, but let your mind wander and you could wind up zombie chow, even if it was day time. The main storyline remained challenging but never went absolutely insane. There were also plenty of optional things to do that made the game more difficult (rescuing survivors, hunting psychopaths or going on a zombie genocide), but rewarded you for it with extra experience, new items or an achievement.