From the NES/SNES period?

U-foria the Saga (NES)

TMNT II The Arcade Game (NES)

Megaman games 

Illusion of Gaia (SNES)

Final Fantasy VI (not by square, I don't trust them)

What is that first game, it looks insane :o

I could totally get onboard with the rest!

I would love a remake of that masterpiece! They could do so much with it.

I would love a Pokemon Stadium remake on NX

Glad to see a Rock 'n Roll Racing mention, loved that game on SNES! xD

Star Tropics deserves a good reboot/remake I think. Doesn't even have to be a retail release, they could do an eShop title.

I'm honestly surprised they haven't made one since 64. On since we're on the topic of Pokemon games on the N64, bring back Pokemon Snap!

It's a Metroid style platformer (but with a map, also not as confusing or insanely difficult XD), pretty great game full of weirdness and charm, it's on the Wii/Wii U virtual console if you like to try it. 

Any of the old nes or snes Final fantasy's would be excellent as long as it's not a miserable portable machine that it gets made for.

Ohh interesting, it looks like it could be super fun! I may have to test it out.

NES:
- TMNT 1-3 (yes part 1 included, seems like it could be dark)
- FF1

Sega Genesis:
- X-men 1 & 2

SNES:
- FF6
- Chrono Trigger
- Secret of Mana
- Knights of the Round
- Saturday Night Slam Masters
- Zombies ate my neighbors