No genre limitation, but the nature of such a question naturally invites more fantasy RPGs than most other genres.
Still, the nature of the question is the same. What game out there felt like more than a game to you? Where you cared about the NPCs, from main narrative to shop clerks? Where you felt a sense of wonder just exploring the cities, lakes, and mountainsides? Where bits of secrets lay scattered behind the most unsuspecting alleyways?
Which games, to you, make you feel you were alive in the universe - as a fellow bystander, not just the 'chosen one.'