In Zelda games, I don't know where to begin as I've played just about every one of them (not counting Four Swords, Triforce Heroes, and the dreaded CDI games)!
Marin from Link's Awakening. Because of the story from that game, I've come to appreciate her a lot more as a character. I'm not going into any spoilers here.
Moosh, Dimitri, and Ricky from the Oracle games. You can ride on those three characters I've mentioned with each of them having unique ways to attack. Moosh is a big blue bear with small wings that can fly briefly and ground pound. Dimitri looks more like a red triceratops that can swim up waterfalls and literally eat enemies in one bite (there could be a rivalry between him and Yoshi here). Finally, Ricky is a kangaroo that can punch enemies. You know, kangaroos are known to have some boxing skills.
Aryll from The Windwaker. She's the younger sister of Link and as a person who is a big brother with a younger sister, this really resonated with me.
Ezlo from The Minish Cap. I don't know about you, but I liked seeing a talking hat that has some features of a bird. And he can help make Link tiny when standing on certain stumps!
Midna from Twilight Princess. The character development with her is well executed and it made me appreciate how she's more than a companion that tells you what to do.
Linebeck from Phantom Hourglass. This guy is known for having love for treasure and sailing the seas. He's also known to have conflicts every time with Ciela (a different version of Navi if you'd like to say that) and I find their bickering to be very funny.
Zelda from Spirit Tracks. If I'm not wrong, this is the first game where you actually go on an adventure with Zelda and sometimes even play as her (I'M NOT COUNTING THAT CDI GAME)! Her personality shows and she's actually scared of rats! Moreover, she can take control of phantoms and use those abilities to her advantage.
Groose from Skyward Sword. At the beginning of the game, he acts like a bully towards Link. But as the game goes on, the character development kicks in and he's not so much of a bad guy after all! Did I mention his theme? It's both awesome and derpy.
I'd also like to add Fi to the list. This sounds controversial because she's known for having no personality and gives out excessive information. However, she's still one of my favourites because all of the information that most other people find unnecessary blew my mind! And while she may be only an artificial intelligence, she stood out a lot from other characters in the Zelda series.
Mipha from Breath of the Wild. I feel like she has a crush on Link. She has healing powers and can be very useful when you run out of hearts. To top it off, Mipha is a zora which in my opinion, is one of the best races in zelda games.