Best Story
Skyward Sword
Skyward Sword may have been controversial amongst many Zelda fans, but here on VGChartz, it's actually quite popular for a variety of reasons. One of these is the game's narrative. Skyward Sword takes place early on in the series mythos, helping tell how the entire conflict of the series began. It did so through some of the series's most cinematic scenes ever, and had an interesting yarn to tell. It should be no surprise then that it wins this category.
Runner-Ups: Ocarina of Time, Majora's Mask
Best Major Characters
Ocarina of Time
Ocarina of Time is arguably the most iconic Zelda game, and one of the many reasons for this is the main cast of characters. Possibly more than any other entry in the series, this game focuses on the conflict centering around the three Triforce Holders, and has possibly the most memorable interpretations of these characters. Link is portrayed as the outsider hero set on a grand quest, Zelda as a fair princess who must adapt to a dark world, and Ganondorf as a schemer who siezes power.
Runner-Ups: Skyward Sword, Wind Waker
Best Minor Characters
Majora's Mask
Whereas other Zelda games tend to focus on the main story, Majora's Mask soujght to create a larger world, most of which was composed of optional content. Among other things, this created a huge cast of memorable minor characters. And I'm not just talking about Tingle! You have the loving yet troubled couple of Anju and Kafei, the various residents of Clock Town who react in all sorts of ways to impending doom, the Bombers, that guy on the toilet... the list goes on and on. Say what you will about this strange game, you can't deny that the ensemble cast is remarkable.
Runner-Ups: Wind Waker
Best Writing
Skyward Sword
Some Zelda games simply don't have great writing. It may be because early iterations in the series weren't always the best translated, or didn't have a major focus on story to begin with. However, Skyward Sword is not an example of this. The game is chock full of dialogue, descriptions, and a generally large script. This script is well translated and crafted, conveying the story quite effectively. Furthermore, the player's ability to make dialogue choices, though minor, further opened up possibilities.
Runner-Up: Ocarina of Time
Best General Storytelling
Skyward Sword
Based on the above four categories, it appears that the favorite story-telling in a Zelda game on VGChartz is that of Skyward Sword. As the entry in the series that devotes possibly the most into its tale, this is a worthy candidate. Sure, the game was a bit lacking in terms of the minor characters, but everything else about the game's tale stands out. I've heard lots of people argue about Skyward Sword's devotion to its story in context to how Zelda should develop. I've never heard anyone say the story itself is bad.
Runner-Up: Ocarina of Time