The initial feeling that the first play through is what ultimately lets me decide how often I'll replay a game. Usually, I'll replay it for the fun factor. Games like the first three (Legend of Zelda, The Adventure of Link, A Link to the Past) are all games that I can play and really enjoy the core elements of gameplay. These are games I can play three or four times a year and not be bored with them.
Other games like Link's Awakening, Ocarina of Time, or The Wind Waker are games that I will play if I feel that I need to refresh my memory of the story. These games are more focused on multiple elements instead of just gameplay, so I play them less often because I hardly have the time to focus on story anymore. I'll pay close attention in the first and second playthough, of course, but after that all I'm interested in is mindless gameplay. So, those are really great for me to replay maybe once a year.
And then there are games I'll replay just because I'm waiting at the bus stop or am on break at work and need to pass time. These games would be titles like the Oracle games or The Minish Cap. Great stories and fun gameplay, but I can set them aside after a half hour and not be worried that I'll forget what just happened in the story.
So, there are multiple reasons why I'll replay a Zelda game, and the game I play is based on those reasons. Like I said, though, the initial feeling I got from the first playthrough will determine how often I play the game. I can replay TAoL and ALttP and LA a billion times because they really, really impressed me the first time. TWW impressed me, but not on the same level, but I'll still play it more often than OoT. TP hardly did anything for me at all, so I'll rarely replay it. And then PH and ST were impressive enough, but the initial playthrough impressed me more with the story and characters than the gameplay, so those two are also games I wouldn't replay very often.