All right, I'll give my thoughts on this. I'll list the partners along their advantages, disadvantages, and my personal opinion.
Navi:
Advantages: Gives decent advice on enemies and puzzles. Allows Link to target enemies and objects.
Disadvantages: Not much personality or character.
Personal Opinion: I really like Navi. I never found her annoying, and thanks to her advice I was able to solve quite a few puzzles, particularly in the Spirit Temple. However, she didn't have too much personality, although that isn't much of a big deal.
Tatl:
Advantages: Gives decent advice on enemies and puzzles. Allows Link to target enemies and objects. Brimming with personality and character.
Disadvantages: None I can think of.
Personal Opinion: Tatl is my second favorite partner character. I found her attitude to be charming and at the same time amusing. I also really like the way her character was done. Her worries for her brother Tael were very sweet, and she really seemed like a good Big Sister.
King of Red Lions:
Advantages: Doubles as transportation. Serves as a guide for Link through the unfamiliar seas. Marks Link's sea chart so Link knows where to go next. Very knowledgeable.
Disadvantages: Cannot follow you into dungeons, thus kind of losing the "partner" feel that previous Zelda games had. Doesn't offer puzzle advice or enemy advice.
Personal Opinion: I kinda like him. He was kind enough to let Link ride him, and he was also an excellent guide for Link as he traveled. However, he didn't really give you that much advice on puzzles in dungeons, nor monsters, considering he cannot follow you around. This was a bit of a problem for me, considering the lack of enemy information often caused me to struggle in battles. Despite this, I still find him an enjoyable character.
Ezlo:
Advantages: Brimming with character and personality. Occasionally gives Link hints as he travels. Allows Link to become the size of a Minish. Very knowledgeable.
Disadvantages: Does not offer good or helpful advice during battles.
Personal Opinion: Ezlo is hilarious. I sometimes just talk to him for the fun of it. The various things he says make me laugh. However, he isn't too good with advice during battles. In the first boss fight, I called him for advice, and he just said, "Don't just stand there! Do something!" ._. This cost him a lot of points, however his great personality makes it hard to dislike him.
Midna:
Advantages: Can warp Link to different areas. Can transform Link into a wolf at will.
Disadvantages: Rude, selfish, arrogant, obnoxious, cold-hearted, annoying, manipulative. Doesn't give a lot of good advice.
Personal Opinion: I hate her guts. She is one of my most hated characters in the entire series. The way she blackmailed Link into helping her by telling him about his friends was just cruel. She basically used him for her own selfish ends. I don't care how much she changes by the end. I literally cheered when she left at the end. She was also a bad helper. She basically just hid in Link's shadow or rode on his back, cheekily telling him where to go, letting him do all the dirty work. I barely found her advice helpful at all. In my opinion, she's the worst partner in the entire series.
Linebeck / Ciela: (It could be argued that both of them are Link's partner in Phantom Hourglass)
Advantages of Linebeck: Brimming with personality and character. Drives the ship Link uses to travel the seas.
Disadvantages of Linebeck: Does not offer advice on Link's quest.
Advantages of Ciela: Her amnesia creates a wonderful enigma throughout the first half of the game. Decent personality and character. Offers plenty of advice on Link's quest.
Disadvantages: Basically a glorified version of Navi.
Personal Opinion of Both: Linebeck's arrogant and self-centered attitude was amusing, and he wasn't rude to the point that he became an unlikable character like Midna. Ciela was sweet, and her memory loss made for a pretty interesting mystery, even if the concept of amnesia is over-used. Both Linebeck and Ciela together, however, make an excellent balance in the game. Linebeck takes over the role of the King of Red Lions, serving as the transportation and waits for Link at the docks. Ciela then takes over and serves as Link's companion while exploring islands and dungeons, which is something Wind Waker lacked. Not to mention, the constant banter between Linebeck and Ciela was very funny.
Princess Zelda:
Advantages: For once, Zelda has a big roll in the game. Brimming with personality and character. Offers advice on puzzles in dungeons. Assists Link throughout his quest. Fights along side Link and helps him solve puzzles in the Tower of Spirits.
Disadvantages: None I can think of.
Personal Opinion: She's my favorite partner character in the entire series, and personally, I think she's the best partner in the entire series. I really liked that for once, the princess actually did something other than wait around to be rescued or wait for the hero to finish his quest. I also really liked her personality, too. She was really feisty, as well as amusing, and the fact that she was afraid of rats was adorable. My favorite thing about her, though, is that she, while possessing the body of a Phantom, actually helps Link fight monsters and solve puzzles within the Tower of Spirits. Now that's what I call a true partner. The teamwork and involvement makes Zelda my favorite partner character in the whole series.
Fi:
Advantages: Offers very good advice on enemies. Offers Link decent advice throughout his travels. Allows Link to use dowsing. Allows Link to use the Skyward Strike. Very knowledgeable.
Disadvantages: Has a tendency to repeat obvious things. Does not have a lot of character or personality.
Personal opinion: I really like Fi. I never found her annoying, although she can be a bit obvious sometimes. However, that never bothered me. She offers detailed advice on enemies, and this helped me quite often in dungeons. And the way she showed signs of human understanding right at the very end brought a tear to me eye. I also thoroughly enjoyed dowsing, which was a very helpful ability. Fi's encyclopedic knowledge came in handy a lot. All these things make her my third favorite partner character.
Those are my thoughts on the various partner characters in the Zelda series.