Specifically I mean like a style or made you love them in the first place, it's a sad reality that when something becomes popular it tends to lose its unique charm for that of a more broader appeal, also as development evolves and creative teams change its not always realistic to expect a sequel to be going for the same feel, even so i think it's an interesting discussion to have.
For me the one that's coming to mind is dragon age, despite some of its flaws, a troubled development cycle and bugs and glitches that to this day haven't been officially patched, nothing has come close to this game for me in terms of what it delivers.
Between the story which really makes you feel like your having an impact, and just the setting in general the sequels haven't lived up to it in my eyes, with 2 being a perfect example of what I was saying at the start, and inquisition feeling weak in other ways, mostly though strange as it sounds I can encapsulate this best with the music, dragon age origins music bursts with emotion, it's bitter sweet and epic, like a lord of the rings movie, you could listen to some of the tracks and straight away know what origins is like tonally, yet the sequels completely went in a different direction, it's a small thing perhaps but is the best metaphor for what I'm talking about I can think of.