1. Zelda II: The Adventure of Link
Everyone loved The Legend of Zelda's then unique top-down, action-adventure style, which defined the genre for years to come. Naturally, Nintendo wanted the follow-up to be something completely unrecognizable. If internet acronyms existed back in 1987, there would have been a lot of WTFing going on.
How It's Different From The Original: I don't think anyone expected the sequel to The Legend of Zelda to be a side-scroller RPG with magic spells, extra lives and a world map. Not to mention a final boss that is literally your shadow. And just in case people weren't confused enough, it was the only game in the series to proactively avoid name recognition by eliminating "The Legend of Zelda" from its title. Also, the graphics were a lot uglier in a number of instances. Such as the instance of "the whole thing."
Fact: An NPC's first line of dialogue is "I am Error." This is a mistranslation of the Japanese word for "Jerry, don't forget to translate this."
Also: This is THE Adventure of Link? I'm pretty sure he had a bunch of adventures. Like, including the one right before this one and about a dozen after.
2. Super Mario Bros. 2
Okay you just made the single best-selling game of all-time, launched what would be the most successful console ever, and made an overweight plumber one of the most beloved and recognized characters in the world. You can finally relax a little, right? No need to strain yourself too much with the sequel. Let's just stick Mario in someone else's game! Not like anyone would have bought "Doki Doki Panic" anyhow.
How It's Different From the Original: Suddenly you're not limited to playing as Mario or Luigi you can play as Princess Peach or Toad as well, and everyone has different abilities and a life meter now. Also, jumping on enemies no longer does anything you have to chuck beets at them. And Koopas? Long gone. Now you have to fight masked midgets and blowjob dinosaurs. And King Koopa? Psh, as if. Now you have to fight a burping frog. Much better. Oh, and it's all a psychedelic mushroom-induced dream anyway.
What?: Yeah, blowjob dinosaur. Excuse me, drag queen blowjob dinosaur.
Also: The Japanese version of Super Mario Bros. 2 was eventually released in America as The Lost Levels, where you found out everyone was dead. But at least they got to go to Best Friend Heaven in the end.