What Could Have Been: Luigi's Mansion was originally going to be the first Mario game ever to be rated T. It was going to feature a much darker story with much more horrifying monsters, one of which was a stereotypical hunter ghost who wanted to kill Luigi and make him a trophy. The mansion itself was much creepier. The biggest change was, if the game was not completed by the conclusion of one in-game day, Luigi would not save Mario and possibly become cursed himself.
The game itself was initially much harder as well. Your Poltergust had an exhaust meter which, if overheated, could blow up and cost you some life. There was also a ghost that could sneak up on Luigi and scare the snot of him, also costing him life. Your map that's included on your Game Boy Horror originally didn't have the feature where you could find the right room to fit the right key in.
Luigi's Mansion was also planned to be in stereoscopic 3D using an add-on, but when the production of said add-on turned out to be more expensive than the system itself, it was canned. In hindsight, it makes sense that when Luigi's Mansion 2 was announced, it was on the Nintendo 3DS, which has 3D without the need for an add-on.