Interesting idea. I'm going to go with my gut responses.
Revive: Star Fox
I think this counts since we're going on 9 years since Star Fox Command. Keep it focused on on-rails shooting with spectacular graphics and colorful characters with catchy dialogue. Like Star Fox 64, multi-terrain vehicles are good too, as an ancillary focus. Take some of the elements from Star Fox 2 and Assault -- a transforming Arwing, the ability to land and jump out into another vehicle -- but make them tighter, with robust online and local multiplayer modes. Incorporate the Wii U GamePad as a place for a touchscreen cockpit console (not the core controls, but Arwing transformation, weapon selection, radar, mic, speaker, maybe some sort of energy routing system to change shield direction/weapon configuration and offset damage, etc.), second screen for co-op/multi or first-person view gyro controls.
I'll stop now. Fanboy dreams run deep.
Reboot: Mega Man
The original little guy. No X, no Legends. Just a neatly designed shooter. I imagine a tightly focused character action game, mostly linear with a little room for exploration. Essentially, Jet Force Gemini meets Resident Evil 4, but a hell of a lot faster with a little less exploration. Take the aesthetic of the Smash Bros. 4 Mega Man design and run with it, or cel-shade it. The story: Dr. Light's benevolent boy robot, Rock, fights some evil-assed robots made by the evil-assed Dr. Wily. He steals their weapons along the way. The end.
Reimagine: Mach Rider
Just because I'm infatuated with this character's design and the post apocalypse (plus it would diversify Nintendo's first-party offerings). I'd like to see this re-imagined with a surreal, off-kilter A Boy and His Dog aesthetic, or perhaps a Fist of the North Star, late-80s anime influence. Gameplay wise, Fallout style exploration and scavenging, with the focus on building and customizing Mad Max-like vehicles down to the tiniest stats, which you not only use in missions, but bring into versus play. Players could also used scavenged materials to design and share battle arenas, in a throwback to the original game's Design Mode.
Remake: Gladius
I just want to see Gladius with current-generation graphics during battle. The addition of more characters, gear and arenas -- as well as fleshing out the game between battles -- would be icing on the cake.