It's not often one hears "Mario" and "worst video games of all time" in the same sentence, but every great game franchise has to have a worst entry, and Hotel Mario owns that title. There have been other games where Mario is not a hero anyone can really root for, but Hotel Mario is hands down the biggest, which perhaps explains why it's one of the most obscure Mario games.
Hotel Mario was developed for the Phillips CD-i (a failed game system you may never have heard of) and released in 1994. Even if it had been the first Mario game, it still would have been hated, but it came along well after the series reached all-star status, making the offense even worse. The game shouldn't have been made in the first place - and it almost wasn't. Alas, creators didn't stop themselves, so the world now has to remember its radiant terribleness.
Even if you think you know everything about the history of Super Mario, you may not know the sad truth of Hotel Mario. Once you find out the truth, you'll probably appreciate how great the series has become.
Hotel Mario is billed as a puzzle game, but really, there's nothing included that even resembles a puzzle. If anything, it's a knock-off of the original Donkey Kong. There's no problem-solving in the game; just avoiding goombas and koopas. The player slowly climbs their way up various levels in each stage, closing each open door before taking the elevator to the next level to repeat the process. To sum up, you close doors. End of game.
In the early '90s, Nintendo wanted desperately to get into the super futuristic world of video games on CD-ROM. Sega beat them to it with the laughable Sega Mega-CD, but it turned out to be a good thing, as Nintendo saw that system fail and decided to back out of their plans to emulate. They had been in the process of developing a system with Phillips, but after Sega's failure, they decided to just give Phillips licensing for a handful of their Mario characters so they could develop a game for the Phillips CD-i. That game: Hotel Mario.
The Phillips CD-i was a gaming system developed in the '80s and early '90s. It's one of the first to implement online capabilities (though they were quite limited given the era). As the name suggests, the games were in the CD-ROM format, but that didn't mean they were good. The Phillips CD-i boasts many of the worst games of all time, including Link: The Faces of Evil, Zelda: The Wand of Gamelon, and Hotel Mario.
NovaLogic was developing a Mario game for the Phillips CD-i called Super Mario's Wacky Worlds, which was supposed to be a sequel to the Super Nintendo's flagship Super Mario World. However, the game was canceled before it was ever released, leading in part to the frantic effort to make a new Mario game for the CD-i, and subsequently to Hotel Mario. The finished game feels like kind of a rush job, and it's often not considered canon, especially because it's unclear where it fits into the Mario universe given the timeline and what Wacky Worlds was meant to be. That said, "canon" is a relative term as most games in the series are largely one-offs.