Best Story: The Wind Waker
I love the more personal stories in Zelda, the ones in which Link's main quest is actually just to save people important to him. Other games do this same kind of plotline, such as Twilight Princess, Skyward Sword, The Minish Cap, and Phantom Hourglass, but The Wind Waker does it best. Link's relationship with Aryll, and his reasons for going on his quest, all seem so genuine. I also love the way the story is told in that game, and how it's so relatable because everybody has a fear of losing family. I don't have a little sister, but I imagine everybody who does have a little sister or brother feels massive feels when they play this game.
Best Graphics: Breath of the Wild
While I haven't actually played the game yet, what I've seen of it looks absolutely beautiful. The artstyle is gorgeous, and the attention to detail is incredible.
Best Gameplay: Twilight Princess
While I hate the Wii Remote controls, I love the way the game plays as a whole. The Hidden Skills are great, if underutilized, and Wolf Link is awesome. This game also features some of the more unique items in the series, even if most of them are virtually useless outside of the dungeon they're found in. I love the howling stones, and how the howling stones make the golden wolf appear in the overworld. I like the Twilight, even if some of the twilight scenes are tedious. And this game has, in my opinion, the best batch of dungeons overall in the series.
Best Sidequests: Majora's Mask
Not only is this game built around sidequests, but each one is fun and engaging to complete. None of them are too overly tedious, none of them are really stale or boring. This is the only game in which I genuinely enjoy completing all the sidequests, and it's just chock full of them!
Best Music: The Wind Waker
This was a really hard one. Nearly every Zelda game has near perfect music all around, but I had to give the slight edge to The Wind Waker, for one simple reason. While I think other games may have better and more fitting themes, The Wind Waker's soundtrack is the one out of all of them that I can play on repeat for hours on end without getting bored, because each song is catchy and dynamic and just enjoyable to listen to in isolation.
Second place would be either Twilight Princess or The Minish Cap.
Best Overworld: The Legend of Zelda
I think most people will probably say Breath of the Wild for this one, but I have not yet played it. I have to give it to the original The Legend of Zelda, because of its massive emphasis on exploration. While The Wind Waker and Twilight Princess have similarly massive overworlds, they don't have much exploration value. Everything is really obvious; in TWW, each square has a different island, so there's no going out looking for new islands to chart, and the islands themselves are mostly small with only one or two small treasures on them; in TP, while there are all the lantern caves and boulders everywhere and lots of enemies to kill, the overworld is annoying to traverse because of all the narrow corridors separating the different sections, and few of the secrets are actually difficult to find. In The Legend of Zelda, there are no hints. We have a huge overworld with tons of areas to explore, and we have to actually look for all the secrets. Finding secrets that are not obvious with few/no hints is a far more rewarding experience than, say, landing on an island and completing an obvious puzzle for a worthless treasure, or blowing up an obvious boulder and following the linear path to the heart piece at the end.
Most original/Least original:
I don't know if I can answer these, because what exactly is it that makes a game original? Ocarina of Time is a fairly generic Zelda game by today's standards, but its innovations were unprecedented at the time. Majora's Mask is possibly the most different game of the series, but how original is it actually when it recycles music and character models from its predecessor? The Minish Cap and Skyward Sword gave us new villains and some neat gimmicks, but they're also pretty generic in the grand scheme of things.
If I had to pick, I'd probably argue that the Oracle games are the most original, since they were designed as partner games, and they introduce completely new regions, villains, and characters. But then again, the gameplay isn't really any different from previous games. The time gimmick in Ages had been used before, and you could argue the Seasons gimmick was original, but at the same time, the concept of alternate versions of the same world had been used in several previous games.
So, very hard questions to respond to, and I don't think I can really come up with a solid answer for either. Each Zelda game is original in its own way, while also each one takes ideas from the previous ones and other games as well.
Best Overall game: Majora's Mask
Majora's Mask is basically a perfect Zelda game in my eyes. While I generally prefer Zelda games to have more dungeons, it's forgivable in this game because everything else that it does, it does really well, and the dungeons it does have are great for the most part. This game is unique, it's creative, it's challenging, it's got a great story, and it's not afraid to admit that it's different. It's chock full of really fun sidequests, the difficulty is basically perfect for what Zelda games should be, the music is great, the story is awesome. I could go on. It's also arguably one of the darkest Zelda games, while it's still just as charming as any other. Gameplay wise, it's really cool. The 3-Day gimmick is something a lot of people criticize the game for, but I think it's one of its best qualities because it forces the player to change the way they play the game and come up with different and new strategies. Overall, it's an amazing game, and I have no regrets calling it the best of the batch.
Best Replay value: Ocarina of Time
While Ocarina of Time isn't overly difficult, it's a solid game, and one that's held up as being one of the best games ever since the late 90's. When people think Zelda, they think Ocarina of Time. This game is really fun, it's easily the one I've played the most, and I never get tired of it. It's among the most replayable of all the video games I've ever played. It's fairly linear, but it's really easy to go off the beaten path and play the adult dungeons in almost any order, and there are tons of different ways to enjoy this game; you can do a three heart challenge, you can do a no goron or zora tunic run, you can 100% it with some difficulty but it's not frustratingly difficult. Even after almost 20 years, people are still finding new glitches and such that allow you to beat the game faster and faster. So I can say with utmost confidence that it's the most replayable game in the series, for many reasons.
Good thread! This one really made me think a bit, so it was fun to respond to!