Hmm, this is a tough one. There's so many, and I haven't even played every single Zelda out there, but I'll try my best!
Sidequests
Everyone will probably agree with me, and I will choose
Majora's Mask. This game was pretty amazing! Sometimes, on my playthrough, I usually think that some of the sidequests are part of the main quest! That's pretty impressive! I mean, to create a game with that distracting of a sidequest(s) is just purely genius. I'm hoping for a Zelda game to come out with that multitude of sidequests.
Bosses
Boss quality has sort of gone to the bottom the last few years. I mean not in gameplay itself, but just in originality and difficulty. But, I'm not grading my favorite game bosswise by that. I'm going to grade it to how memorable the boss battles were. When it comes to that, I'd have to say that my most memorable boss battles were in
Twilight Princess. The pure scale of the boss battles were nothing short of epic. That said, it's difficulty was the one that came short of my expectations. I mean, you see a giant Fyrus right in front of you, and the first feeling you get is intimidation. After few minutes with the guy, it feels like you'd rather fight a bird; yup, that's how easy it was. But again, these bosses were pretty memorable. The only times you get to fight a dragon was in The Legend of Zelda, with all the Gleeoks. In Twilight Princess, they one-upped it by adding Argorok. Again, it was an embarrassment with the difficulty, but the experience just took my breath away. Don't even get me started on the final boss.
Weapons
What's Link without a weapon, right? It's been a while, but I'm going to say
Minish Cap has the best items. The concept of building the Four Sword was amusing to me. And how can you forget about the Gust Jar, Roc's Cape, that Cane, and most of all Ezlo? That was quite interesting, right? They were pretty useful, as well (*cough Twilight Princess cough*). They also added more flavor to the puzzle-solving and the gameplay. The weapons/items produced that Metroid feeling where you need to get something in order to get past a certain barrier. That also adds a sense of curiosity as to what's hiding behind that obstruction. It then stimulates your head and gets you thinking, contributing to the sense of exploration
Story
This one
easily goes to
Twilight Princess. To all of you who don't agree, I see why, but let me try to change your thoughts. Twilight Princess had a solid story, well at least in the near beginning. With Zant acting like the boss, and taking control of Hyrule single-handedly (well, that's what we thought at first). He was so mysterious, with his creepy mask, increasing the intrigue. With the dark atmosphere, everything just contributed well. I've been dying to see Zelda take the dark side path, but I guess it's not going to get darker than Majora's Mask, right? Anyways, to get back on topic, Twilight Princess had some nice characters to interact with, and it also had a VERY surprising twist. I'm pretty sure that almost no one ever saw the twist coming. But that twist happens to be what broke the story for people, and I understand that. But that aside, the Dark Interlopers really interested me. It piqued my interest, and has ever since. It should, hopefully, be quenched when Skyward Sword is released.
Overworld
This one is no contest:
The Legend of Zelda. This game had it all! Secret caves, hidden caverns, Moblin hideouts, and secret shops, scattered all over the Overworld. This is probably the only game that also had invisible places (path to the secret rupees, remember?)to explore. This game truly is what set the exploration factor in the Zelda series, and I hope that Nintendo tries their hand at making exploration like this in other Zelda games. I mean, come on, there was a dungeon that was literally hidden! Yes, I'm talking about Level 8 here, that one that you had to burn the tree. I believe it had a disappointing mini-game, but the overall game and exploration more than make up for it.
Dungeons
Ocarina of Time takes this spot! The dungeons posed a lot of challenge, and were brilliantly designed. It truly lives up to the bars that previous Zelda, and Nintendo games out there. The Water Temple was pretty frustrating with all the changes of the water levels, but it's okay. The puzzles presented in these dungeons were also fun, inventive, innovative, and gave your brain a hard time! There's nothing more to say about this. Ocarina has the best dungeon design, and that's that!
Characters
I've never really played it, but
Wind Waker takes the crown in this area. It has arguably, the best depiction of Ganondorf. I mean, yeah, he's a fat guy, but he had the most feelings of any Ganondorf out there. The other characters are no pushover either. Tetra, anyone? Yeah, she was the boss, and didn't have any princess-like traits to her. She was still that same pirate who lived for exploration. Link, well, this is something I NEVER said, but Link had character in this game! Like above the post before this one, they had nice expressions. It didn't make Link a separate character from us in which we couldn't fill in for him, but it still showed his individual feelings, nearly mirroring our own if we were in his situation.
Design/Art Style
I'm a big fan of anime, so I'm going to hand this to Twilight Princess. Sure, the world's weren't "colorful" but the whole concept of the art is simply gorgeous! Lake Hylia was the best Lake Hylia ever! It was just gorgeous and breath taking. I can spend a long time in Hyrule Field killing some Moblins(?) while taking in the beautiful scenery of every unique provinces. The character designs were pretty good, too. This Link looked even better than Adult Link from OoT, and is better than Link in SS, IMO. There were some pretty weird looking characters, too, and that added some humor to this dark universe. The art style also goes along well with the story, so...:yes: :yes:
Anyways, that's my opinion on which games should win which category! I hope you found this post helpful!