Sonic, no doubt. I think that Nintendo could do great Sonic games, because, obviously, Sonic Team doesn't know what to make of it. And Nintendo has a lot of experience with platformers... I would also buy Bayonetta IP, fun games and different to what Nintendo has to offer.

If Level 5 isn't making another Ni No Kuni then give that to Nintendo. It seems like it could belong there, tho Ni No Kuni on PS4 would be so much sweeter.

They should own every Level-5 IP, specially the (3)DS ones, otherwise those games are going to shit with mobile.

Megaman for sure if it were a Legends game or something in the same style. I wouldn't like to see another 2d platformer... or even 3d at this point. Something action adventure/action rpg would be great to see on a Nintendo console which they could easily do with Megaman and would fit well with their already existing IP.

I could also totally see a Castlevania reboot with gameplay similar to Lords of the Fallen being a good choice. More mature and at the same time sort of kid friendly(castlevania). I know a lot of people have a hard-on for Bayonetta, but I doubt the bondage chick will continue to be a Nintendo exclusive.

Sonic. I'd like to see what they would do with the games since Sega really hasn't been treating the IP well.

Call of Duty. Why? Marketshare.

Nintendo. For the love of god revive Eternal Darkness. Do it now!! Lots of love, RedInker.

Bayonetta, Mega Man, or Sanic. No Banjo, since the original devs probably wouldn't come back, what with the spiritual successor to tend to.

Answering this question from an emotional and "this is more Nintendo than not" point of view rather than a business point of view:

Banjo-Kazooie: A few of Rare's IP's would be welcome back into the Nintendo family, but I feel that this one would work better than Conker, Killer Instinct, and Perfect Dark. Banjo-Kazooie is indeed another kid-friendly platforming series, but I feel its unique blend of 3D open-ended collectathons would complement Nintendo's other games well. The 3D Super Mario games have largely gone in other directions since Sunshine, so this style of games would not overlap that much with existing Nintendo series. The dynamics between the major characters work well enough even in gibberish to give the games their own personality distinct from Nintendo's existing series. We'd also get a good candidate for Smash Bros. And besides, the two main games and the non-Nuts-and-Bolts spinoffs were Nintendo exclusives anyway, so unlike with series like Castlevania, there wouldn't be much in the way of depriving fans of other platforms.

Honorable Mentions: Professor Layton, Mega Man, and anything popular on the NES or SNES that has become disused ever since.

Mega man, sonic and banjo. BUT, no 2d games allowed till awesome 3d ones are made. Then 2d downloadable titleswould be cool. But retail versions on hanheld only. Its 2015, Aaa 2d games are are basically an oxy-moron in myopinion.