Definitely Zelda from Spirit Tracks. Not only did I not find to be irritating or bothersome, but she was also helpful beyond simply giving information. I'm referring to, of course, her ability to possess Phantoms in the Tower of Spirits. I found this to be an interesting concept that was well implemented in this case. Truth be told, it was one of the things that got me to buy the game. Not only do I have the ability to control a Phantom, a powerful enemy that gave me a hard time in Phantom Hourglass, but I get to do so as Zelda, who is accompanying Link in his adventure. Although Zelda has expanded outside the trope of Damsel in Distress in previous titles, I feel that this one deviates from the norm the most in a good way.
I'd be happy to see concepts like this in future games. The companion doesn't necessarily have to be Zelda, and his/her ability doesn't have to be possessing Phantoms, but something along those lines that expands upon how it was done in Spirit Tracks would more than likely be a selling feature of a new Zelda title.