I... am the person who seems to fall for the most obscure games ^^;
The original trilogy of Thief games:
It's my all time favorite series, even though there are parts of it that scared the shit out of me the first time I gave it a try. I put it aside for years until I was brave enough to try again and I enjoyed it to the fullest
It's not perfect, but to me it means a lot. I love the protagonist (Garrett's quality sarcasm XD), the lore and how dark it is. Steampunk aesthetics, horror elements. The fact that it focuses on stealth and not combat. The humor and the missions. I once tried to explain which mission is my favorite and ended up talking about the game for hours to my friend XD
I maybe met 3 people in my life who knew about it before Thief reboot came out, and yet it's still hard to find some fans to talk about it XD
Other honorable mentions are:
Claw - about a cat pirate looking for the amulet of 9 lives. It was the first game I ever bought for PC, and it was fantastic! It scored some nostalgia points.
Theresia - A... disturbing nintendo DS game, it's one of those escape games (psychological horror visual novel adventure game, thanks Wiki). "Dear Emile" is about a girl in the middle of an abandoned military complex that happens to be infested by a strange plague and "Dear Martel" is about a doctor struggling with finding his way out of a hospital.
Disciples Sacred Lands - a really obscure turn based strategy game, but it was the first I ever played, and I enjoyed it. I honestly don't remember the plot anymore, but it has a high nostalgia value in my heart XD
Iji - a freeware gem made by one dude (aside for translation, music and dubbing). The world is invaded by aliens and a girl named Iji was genetically modified to fight hem. Nanomachines! It has a good story and an amazing amount of bonuses and secrets and little things that are wonderful.
There's a lot of other titles but I think these are my top faves.