I prefer games to be normal-hard, since I want a little challenge but I don't want to be flipping off the screen every five seconds in rage.
But as everyone says, it depends.
Mario (not talking about RPGs) - I rather keep it on the easier side. It's meant to be fun and for the family, not challenging (imo). The sports games can be hard if they want, but keep Kart and Party relatively based on who's playing and not due to the game itself.
DK - I think that the DKC games are really great in difficulty and I like that I have to try a few times to get it. Not sure how I feel about the levels where it doesn't matter except for timing.
Zelda - I want it to be difficult in the puzzles. I want to feel like I accomplish something when I can go through a temple, like the Water Temples of OoT and TP. I really don't mind the fighting being on the relatively easy side, because SS had some enemies that were just annoying to fight because you have the instinct to just swing and sometimes the control does not like to cooperate.
Pokemon - I think it's perfect in terms of challenge for me, at least when I'm vs.-ing friends.
Pikmin - Oh man, Pikmin is such an excellent series for skill level. You can kind of set your level by how quickly you try to move through the game. I think the base level of difficiulty is already on the normal/hard side, but you can make it really tough. Pikmin 2 definitely was the hardest and Pikmin 3 is probably the easiest in terms of the enemies, but Pikmin 3 challenge mode is great for really pushing yourself.
Fire Emblem - This game might be where I need to pull back a bit since it requires not losing any of your members, and lots of soft resets. The beginning is usually rough for me since my men are at a low level, but usually by the middle-late chapters I am fine.
Those are like the main games I play in general, with a few exceptions.