Legend of Zelda was...well, different compared to a typical Zelda game. Not only was it enjoyed by everyone (even from rather harsh critics), it was something which proved Ninendo is great at keeping their franchises fresh.
Saying that, I think some of the bigger series will be given the same treatment as well. Chances are Kirby, Pikmin, and series similar to it will just keep evolving its great gameplay. The bigger franchises like Mario, Donkey Kong, Animal Crossing, and others may be different than what we typically see.
Pokemon: Sun/Moon was rather different than most Pokemon games. It didn't have much to do after the game, but it had an excellent main story. Unfortunately, the 3ds severely limited generation 7. Gamefreak honestly was hurt by having it on the 3DS. With the Switch, their budget will most likely be bigger for multiple factors (including the bump from 240p to HD). This is a strange theory, but I believe they have been working on a Pokemon game for the Switch at the same time as Sun/Moon. Either that, or they are just gonna make a modest entry to test out the Switch and then try to make generation eight huge.
Either way, I think Pokemon can keep on evolving. It is great, but improvements in the quality of the games will always be welcomed. I really enjoyed soulsilver for being able to visit two regions and having ridiculous amounts of post-game content- hopefully the Switch will have a S2/M2 which will let you go to Kanto to visit Lillie (it'd work with the story).
Donkey Kong: Donkey Kong is a great series. Tropical Freeze was one of the Wii U's only good games, and it really shined on a dull console.
As great as it is, I was always curious on whether a 3D donkey Kong would work. Would Donkey Kong benefit from moving away from its current style, or would it ruin what makes Donkey Kong great?
Animal Crossing: Chances are there was an Animal Crossing U in mind, but it was quickly stopped. AC is a great, there's no doubting that, but it is obvious that more power gives us more oppurtunities.
I think Nintendo should really focus on Animal Crossing. New Leaf was amazing, and a worthy successor would be another addition to the Switch's lineup. A bigger world or game-changing features can really improve this franchise.
Metroid: We have constantly been teased about a new game, and chances are we may get one. If we do however, will it be classic Metroid or something more along the lines of Prime?
I think Nintendo will make a game similar to Prime to make a wider audience for the Switch. It will help more hardcore gamers see some interest in a mature Nintendo game. What does Nintendo need to do to accomplish this? Only one thing- they need to make a Metroid game (no- federation force doesn't count).
That's about it- my ideas probably aren't revolutionary or anything, but it is an interesting topic.