2020 I hope. I think they can build on BoTW and do even bigger things.

Re-using the Breath of the Wild engine, and some assets, and possibly using the same Link, I'd say late 2020. A direct sequel in the vein of Majora's Mask or Link's Awakening: so an odd, unusual Zelda game set away from Hyrule.

We might get a remaster before then. Either Skyward Sword HD (2019) or Link's Awakening 3D (2018).

Id say 2020 except they will make a similar game to BotW except a co-op version. It needs to be done Nintendo

Switch will be only Nintendo system and hardly they will be releasing any other Zelda on 3DS, having that on mind I will say 2019., we could have easily 2D Zelda game also, Aonuma actualy said that: "2D Zelda On The Switch Is “Definitely A Possibility”.
http://www.gameinformer.com/b/features/archive/2017/02/14/a-2d-zelda-on-the-switch-is-definitely-a-possibility.aspx

Instantly, I want to say: 2021
So, that would be my guess.

Probably at least five years for a "proper" release, now that there is no dedicated, low power (withhold jokes about Switch being a glorified portable that VA outputs to HDTV) Nintendo development platform. I don't see 3DS consumers getting another major Zelda game, but who knows?

With no dedicated handheld development platform, it would seem a bit odd for Nintendo to let the Zelda IP go silent for five years, but my impression based upon the season pass model implemented that has worked for other open world games like Witcher 3, is that Nintendo would like to stretch BotW for at a least a year after initial release with updates/DLC.

Nintendo could potentially do a Majora's Mask style game (that used Ocarina of Time assets as the base) that uses the same game engine, assets, basic play mechanics, etc. of BotW in an all new adventure for the Switch in 2, maybe 3 years tops.

Otherwise, we may only see a second Zelda game for the Switch (a proper $60 MSRP release) just as the platform is winding down in five years (2022).

No spinoffs or side series in my list. So nothing in the Celda trilogy (WW, PH, ST), or Majora's Mask.

Are you serious? Majora's Mask and Wind Waker aren't spinoffs or side series; they're fully 3D, mainline Zelda games. Do you not actually know anything about the Zelda series?

This makes little sense. If you cut Majora's Mask you'd need to cut Adventure of Link as well for the same reason as that game is, just like Majora's Mask, just a continuation of it's parent game; the original LoZ. Actually, MM and AoL are also the same type as Link's Awakening whose only crime is being on a handheld, but I could see why you'd leave out MM and LA, it's just that that means you'd also leave out AoL. Then, Wind Waker is one of the main chapters, there's no argument. It's stupid to claim otherwise. I hate on the Wind Waker pretty much every chance I get but even I know it's on the same level of importance in the lore of the series as the other "main" games that are LoZ, ALttP, OoT, TP, SS and BotW. As a side-note, one could argue that The Minish Cap is also one of these main games, because it started it's own chapter in the timeline and it's own line of sequels. WW is in no way a side-story or spin-off. Besides, Crossbow Training, Tingle and Hyrule Warriors (so not even games like MC, PH, ALBW or whatever) are the actual spin-offs.

And lastly, A Link to the Past is not and is not called "Zelda 3".

I'd assume that they're already at work on the next game for Switch. Probably gonna see it ready for the Holidays in 2019.