Well, let's see... I like that one Hex Maniac in X/Y, who upon being defeated breaks character and admits that she isn't sure
how a Hex Maniac is supposed to act. The Hex Maniacs in general in those games say some really strange things, including one who I believe says something along the lines of having known since her past life that she would someday battle the player character.
I also like how the NPCs seem to be getting more self-aware as the games go on, with that line of people in B2/W2 who basically admit that they're there for no reason and will someday vanish without a trace, or that one guy in Terminus Cave in X/Y who comments on how one of the Hikers in the cave has been walking back and forth across a bridge for days. Maybe in a future game, the main villain will be an NPC attempting to defeat the player character so they can steal their position as the protagonist?
I'll also mention Maid Julia, AKA that one maid in the Battle Chateau who talks like a robot. I wonder just what the deal with her is.
There's also an NPC in X and Y you run into late in the game who apparently got lost on the way to the Trainer's School, and
somehow ended up on Route 18. One has to wonder how that happened. Similarly, there's an NPC who went on a walk with her Furfrou, and said Furfrou ended up leading her all the way from Couriway Town to Courmarine City.