I like the story, the characters and the adventure element. I think the freedom you are allowed in games like Windwaker and Twilight Princess as far as exploration goes is pretty sweet. One of my favourite things has to be the music though. I love the scores to the games so much!
I can't exactly pinpoint why I like Zelda so much... I think it's all of those elements! They create the perfect storm. Perhaps what I enjoy the most, though, is the way Zelda makes me feel, like I'm part of a bigger picture. For that, I choose adventure and story
Zelda is so intrisicly linked to my childhood it's impossible for me to think of it without feeling immense nostlagia. @Eternal Legend I definitely think that's true of LttP, OoT, WW and TP. The more territory you have to cover, the more you can get sucked into that world.