There are two games I would love to play for the first time again and those are Portal and Dishonored.
Portal is obvious - it's a well-refined and immersive puzzle game with enough story and atmosphere to keep you invested, but never so much as to pull you away from its puzzles. It may only be a short game, but it is one of the best!
The only people I know who haven't given this game the upmost praise are those who've never played it before.
Edit: Portal 2 is also a fantastic game, but it definitely leans on the story more. That is by no means a bad thing though, as we wouldn't the absolute menace that is Cave Johnson without it.
As for Dishonored, the original is Arkane Studio's best game IMO - the world it's set in is so interesting and brimming with lore; the levels are well crafted, and reward the player's creativity and exploration without ever feeling forced; The gameplay is challenging, but without ever feeling overwhelming. I'm sure it has it's flaws, but all these years later, I still remember how much it got right.
Edit: Dishonored 2 was very much like it, and I remember it for all the same reasons, but the first is the one that really captured that lightning in a bottle for me.
I also loved Prey. It plays in a similar style without feeling too much like it's predecessor. I can't say I liked the Roguelike DLC very much though.
Edit 2 Electric-Boogaloo: I keep forgetting Dishonored uses the American spelling. I always remember it in the British spelling. Oops.