I'll update with links when I'm on my comp next (mobile now), but a few off the top of my head:

Portal 1 and 2. It's so popular that it doesn't seem like it even can be 'unique', but the game play really is one of a kind, and it's pretty great.

Enderal - total conversion mod for Skyrim, but in the steam store as it's own game. It's got familiar combat and game mechanics, but the antagonists aren't your typical big-bad-evil-guy, but things like emotions, mental states, and philosophies. Somehow they managed to work that kind of content into a fantasy RPG... it's a fucking masterpiece, and it's free if you have Skyrim in your library already (it uses Skyrim's assets and engine, but is not related to Elder Scrolls in any way).

Zelda Majora's Mask, for the N64. This game is fucking weird, even by the Zelda franchise's standards. Every scene is bizarre in a way that other games haven't hit before or since Zelda MJ. It's built around the Kübler-Ross 5 stages of grief; it never draws attention to that, but guides you through them beautifully.

Secret World Legends. Technically an MMO, but treat it like a single player RPG - the MMO elements are shit. This game will have you running all over the globe to basically do Men In Black shit, but instead of aliens, it's occult weirdness, and things like urban legends that turn out to be true. Heavy Lovecraftian influence. One of the more challenging parts of the game are investigative missions, which I'd encourage you to give a solid effort before turning to the web for answers. The objectives can be something like "investigate the murder of John Doe" ...and that's it. You have to tackle it the same way you would IRL, so you'd go to places that make sense like a police station or town hall. It doesn't tell you, which makes it probably the most intellectually challenging games I've ever played. If you dive in, you'll need to choose a faction when you make your character: and trust me in this, choose Illuminati. The story writing is way better than the other two for their faction-specific missions; and the rest of the game doesn't change by faction (you'll be in the same zones, grouping and working together with players in other factions; there's just a few off-shoots of solo faction story time)