HyperRogue – A non-Euclidean roguelike
roguetemple.com
roguetemple.com
Another non-Euclidean approach is that taken by Vicious Orcs: each individual room is Euclidean, and the player can't tell that he's moved from one room to another, but the connections between rooms are arranged such that the overall map doesn't fit in a plane or even a 3 dimensional space. I got very lost and did not finish the game.
Jacob's Matrix is interesting because it actually displays a Jacobian matrix describing, somehow, the way that the pieces of the world are put together. Walking from one piece to another can cause you to be rotated or mirror-imaged. You can also create portals (as in Portal) http://www.zincland.com/7drl/jacob/ http://www.roguebasin.com/index.php?title=Jacob%27s_Matrix
Here's another one. This one deserves mention because it turns out that enemies path-finding in a non-Euclidean space will run circles around a human. At least, I think that's how they do it. I have never felt so humiliated by a game AI. http://www.zincland.com/7drl/kobold/ http://www.roguebasin.com/index.php?title=Smart_Kobold
Although, that being said, someone who spends a lot of time in caves may be better.
1.http://gamasutra.com/view/news/245334/Desuras_parent_company...
There is also an Euclidean mode, where you can see for yourself the things which do not work.