What are some games where getting good at it actually increases the amount of fun you can have with it?
Pic highly related, I've been replaying DMC4:SE for quite some time now and the better I get at it the more I'm sucked into it. The game may not be crazy with in terms of set pieces like Platinum games but I feel like the better I get the crazier shit I can do.
Godhand and Dark Souls is a given. I don't mind any other genre, even racing like DiRT Rally.