Hard to describe it exactly, but basically third person action/adventure games. Any game that gives me a large, detailed, and interesting world to explore, puzzles to solve that are integrated well into the gameworld, items to find, interesting NPCs to talk to and/or help, and a simple action-based control scheme. Mostly Zelda-ish games, though some RPGs fall under this umbrella as well - RPGs that don't inundate you with too many numbers and don't have generic copy/paste level and NPC design.
Games I would fit in this category:
3D Zelda
Okami
Demon's Souls
Shadow of the Colossus
Possibly Ico as well, though it's kinda borderline given the smaller scale of its gameworld and its emphasis on platforming. And neither Ico nor Shadow of the Colossus have many cool items to find, but that's the least important of my "rules" I suppose.
