Hilbert Hotel
It was a dark and stormy night, blah blah blah.
Hilbert Hotel is based on the
Grand Hotel Paradox proposed by the mathematician
David Hilbert. Don't worry though - the game requires zero math skills to win and have fun, but the setting of an infinite hotel was intriguing enough to win out against a bunch of other great settings.
The code for Hilbert Hotel started out as a "game" called Madhouse where you wandered through an infinitely regenerating house of maddening details chasing a villainous scoundrel. As you moved through rooms, items would appear and disappear, your name would randomly change, and sometimes your enemy would randomly die only to be replaced with a new one.
From there, it quickly (medium-quickly) evolved into the Hilbert Hotel that's alive and well today. There's an actual cohesive story - and dialogue! All the comforts of modern technology.