They're a lot harder now that people have more and more ways to datamine games both old and new, but here's some neat ones that come to mind:
Fez's black monolith which someone mentioned above (I wrote the article Ethan from Kotaku references in the article linked above (
https://killscreen.com/previously/articles/immortal-mystery-fezs-black-monolith/) so this is a subject near and dear to my heart)
I recall people spending a lot of time trying to figure out if you could become a werewolf in Bloodborne. On that matter, even though Miyazaki kinda ruined it, in the original Dark Souls there was some sort of item or key that had no use, but of course people were convinced that it had to do something so they would have it equipped at all times and try every interaction with the world possible to see if it would trigger something.
There's that weird frog ribbiting sound in a particular hallway in The Last Guardian that people thought was going to end up leading to something.
The book at the bottom of the bottle level of Super Mario Sunshine is probably an all-time favorite game mystery for me. So tantalizing!
Inside has some REALLY fascinating stuff in its background textures and hidden in filenames and the like.
There's a button in Halo 1 that if I recall nobody was able to determine what exactly pressing it did.
