I think for me the biggest thing is not what 3D Zeldas had, but what they didn't have.  To me the first NES Zelda is the right paradigm, which means it has 4 things: open world exploration (non-linear), lots of secrets, fantastic action (challenging), gradual increase in power (especially through items).  When the first NES Zelda came out it was the best game in all 4 areas.  Since then there have been Zelda games that have surpassed the original in one or two of the 4 areas, but never all 4 at the same time.  Zelda 2 and Hyrule Warriors have great action, but they aren't really that good in the other 3 areas.  Link to the Past has more items and a bigger world, but it is more linear than the original game and the action isn't quite as challenging.  Breath of the Wild goes above and beyond when it comes to exploration.  Not only is it the best open world Zelda, but it is just the best open world game period.  But you mostly have all of your abilities from the beginning and I don't find the combat to be that engaging.  All of these are the Zeldas that I really like.  They are great, but I still like the original the best, even though I'd like to see it surpassed one day.

And then you have all of the other Zeldas, like Wind Waker.  (I'll choose that one since I actually completed it.)  It just doesn't have anything for me.  The action is terrible and not really challenging, and the items help you solve puzzles and unlock new areas, when I really want them to make me better in combat.  The exploration is the best part and even that is disappointing because everything is so spread out that it takes a long time to get to something new and interesting.  The worst part about the puzzles is that they are meant to be a substitute for combat.  So the game has nothing for me.

I don't mind puzzles in and of themself, but I think they have to be implemented right.  I liked how the shrines were handled in Breath of the Wild even though most of them were puzzles.  That's because they were generally one puzzle and then you get the orb and move on.  To me the shrines were as much about exploration as they were about the puzzle, because part of the challenge is just in finding them.  That made it feel like they were following the spirit of the original Zelda while finding an unique (and even improved) way of doing exploration.  On the other hand I didn't like the dungeons in BotW (other than Hyrule Castle which was perfect).  I thought the 4 dungeon designs were lame and I wanted to overcome challenging enemies in them instead of puzzles.  Also you have to solve all of the puzzles to get through the dungeon which kind of sucks, since that totally impedes your progress.  The shrines were better since they were optional and even if you don't figure the puzzle out you could just leave if you wanted to and come back later.  

So I'm basically saying that I don't mind if Zelda includes puzzles (especially how they were handled in shrines), but I just don't want Zelda to be about puzzles.  I don't want it to be an adventure game.  I want Zelda to be an open world, action RPG.

Thanks, this is a great and specific explanation about your preferences. It obviously differs from my preferences, as we are different persons. But I'm not sure about my preferences so much as you, you have seemingly a clear understanding. The thing clear for me is, I love exploration, if I can discover things that I could've missed if I didn't look. Linearity vs. Open World is not so important for  this, but obviously an open world game has a much easier time hiding stuff. The possibility to miss things (which means stuff I have to find and to do to beat the game can't count for me as discoveries, as you always have to find them in order to beat the game) is very important to me, as this gives me the needed challenge to feel good about the achievement. Obviously this works so extraordinarily well in BOTW, thats why I love the game. I agree on the shrines, the sheer mass of them clearly communicates that they are optional and they are usually not a series of puzzle-challenges, but only one. But the Korok-seeds work for me too as possible discoveries, and also finding and talking to people in the wilderness or finding a beautiful scenery is also fine.

On the other hand I'm pretty unclear how I stand towards action. In many games I outright hate it (probably because I suck at it and it feels frustrating). In most Zeldas I don't mind much, or it just fills an otherwise empty and more boring world. In games like Warriors, Monster Hunter and Souls I really like the fighting though. So, I cannot really tell which parts about action and fighting in games I like and which I dislike.

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