Welcome to Remake, Please! where I go on about remakes I'd love to see happen and how they could be an improvement over the original title.
Zelda II: The Adventure of Link (NES)
Would you believe there was a Zelda title that made some big changes long before Breath of the Wild? Zelda II: The Adventure of Link did away with a lot of stuff from the original game. The overhead gameplay perspective was tossed out the window in favor of side scrolling action. This along with Zelda II's high difficulty is the reason most fans dislike Zelda II. Yes, Zelda II is tough (the original Legend of Zelda can be quite the ball buster but fans still love to praise that game and overlook it's numerous flaws) but I definitely don't think it is a bad game, though you wouldn't catch me complaining if a remake made the game far less punishing.
Whenever you lose all of your lives in Zelda II, you get sent all the way back to the palace that Zelda rests in. In a game as tough as this one, that is extremely cruel. Restarting in the level your perished in after a game over would alleviate a great deal of frustration for a lot of players. What would also help are more extra lives to uncover, more health and magic recovery drops
I do enjoy Zelda II's 8-bit sprites and I'd love to see them updated along with the game's soundtrack, which has some of my favorite themes in the entire series history. It was nice to have Super Smash Bros. arrange two themes from this game, but the battle themes, town music and overworld theme are in desperate need of remix love.
Super Mario 64 (N64)
While a big aged, I still come back to Super Mario 64 every few years and have a blast every time I run through it. Yes, yes, it got an enhanced port on the DS but Super Mario 64 was designed to be played with an analog stick.
Nintendo has been more than happy to give two of Link's most memorable console adventures the HD treatment while Mario, the company mascot, has been left out in the cold. With everything Nintendo has learned making 3D Mario titles since Super Mario 64, just imagine how improved the plumber's first 3D platformer could be in HD. Tighter, less wonky feeling controls for swimming and flying with the Wing Cap, which even I have to admit after all these years could be done a lot better. One of Super Mario 64's biggest problems was the dang camera angels, but to be fair, every 3D platformer from that era suffered from this, Camera angles today aren't perfect but much better than they were back then so I'd love to play this game with much more desirable camera views.
An HD remake of Super Mario 64 could take elements from the DS version with Luigi, Wario and Yoshi being unlockable, playable characters. I adore the game's soundtrack but I'd love to see it get the orchestra deal that both Super Mario Galaxy games got. Heck, we've already heard a few of Super Mario 64's themes redone in those games. Can you imagine what Super Mario 64's Water music would sound like with a full orchestra? I'm getting chills just thinking about it. Come on, Nintendo, lay off of Link in HD for a while and give your boy Mario his time to shine.