Depending on how stuffy you get about the distinction between video games and visual novels, Steins;Gate.
It doesn't have as much "gameplay" as another non-combat visual novel I'd include, Zero Escape: Virtue's Last Reward, but I loved every second of it and the subtleties of how the different endings got triggered were a lot more surprising and interesting than in, say, BlazBlue.
LittleBigPlanet. 2D platformers as a whole I'd like to include, because I'd question how jumping on the heads of cute creatures necessarily qualifies as "combat", but on a technicality the boss fights in Super Mario or Sonic almost assuredly disqualify them. Most of the "violence" in LittleBigPlanet is brought about as a secondary effect of the player's actions rather than something you directly do, though, and it's a quite fun mix of puzzles and platforms.
Super Monkey Ball. In an interesting fusion of tilt-table puzzles and, to some extent, time-trial racing, Super Monkey Ball is probably one of the most "game"-y games I've played, as it eschews most semblances of story, context, cutscenes, and things like villains or conflict and just throws you right in to have fun. Brilliant!
EDIT: Oh, and of course Journey and Flower. I'd like to see some of thatgamecompany's work reach the PC.