I like enemies that take a vicious, direct assault, and return it to you. My favorite fights in Twilight Princess were with the Dark Nuts, who I knew could be defeated quickly by carefully timing attacks, but I had far more fun with by charging in and swinging my sword all over the place even though they blocked most of the attacks.
I like creating things too. When a video game has a crafting mechanic where you combine different things and thereby create new things, I'm all over it. Cooking is like this too. That's the kind of "little" mechanic that can just totally steal me away from the rest of the game as I make pies and cakes. Runescape did this, and Rune Factory 3 and Summon Night Swordcraft Story.
I really like it when there's extras on the menu too. Like when they have little character synopses, and extra tidbits about the world and lore, and maybe even little making of videos. I think Prince of Persia included some making of type videos on the disc, didn't they? I really enjoyed that a lot. Age of Empires II had an entire section in the menu for straight up History, which I believe I read over fully twice and spot read another three dozen times. That's one of the main reasons I didn't like Age of Empires III very much, because it lacked that kind of dedication to history and accuracy.