For those who have been living under a rock, four years ago Valve released a game called Portal. This game was groundbreaking: a mind-bending First Person Puzzler, all centered around the idea of creating portals connecting two points in space.
But Valve didn't stop there. The game was already new and fresh, but they decided to sprinkle in an interesting story, one which fits our mute hero well. It's very difficult to create a story which requires next-to-zero interaction from the protagonist rather than just moving forward, but they managed it. The whole time in the "testing environment", a disembodied voice gives hints, help, and provides comic relief. Only to pull the twist once you reach the end: the cake is a lie.
That disembodied voice isn't so disembodied as you thought, and it turns out she's a passive-aggressive machine bent on testing subjects for her own amusement (when she's not releasing deadly neurotoxin).
All in all, the puzzles stay fresh, and then applying them outside of the standard environment makes the final areas memorable. I recently re-played the game and still enjoyed it thoroughly.
Of course, the real reason for this post: now there's a Portal 2! So much science to do, so little time.