Ever since I played A Link to the Past back in 1992 the Legend of Zelda has been my favourite series (Metroid being a very close second) and to this day I still love going back and playing the games over and over again.
There isn't one particular reason that I love the series but a big part of it would be it's basic premise of a hero fighting through and rescuing a princess. It's obviously such a simple premise but Nintendo (and at times Capcom) manage to create such huge worlds and characters and story that it becomes so much more. Take the sidequests for example, especially in Majora's Mask, where you travel around interacting with characters and expanding on this world that Link inhabits and most of the time must save from devastation, it's just immense.
You could argue that each game seems to be the same and yes, to an extent the basic game play is pretty much the same for each and every game but again, it's what happens within the game that makes it so different. Just look at Ocarina of Time compared to Majora's Mask. Basic premise of Link having to save a land (Hyrule and Termina) but yet the games are so different in their game play and style. Ocarina of Time seems so innocent with Link starting out as a child at the beginning of the game before everything goes to hell and yet when he grows up and heads off to destroy Ganon he still retains the innocence and of course at the end when Link and Zelda are young again it comes back in floods. Majora's Mask on the other hand is the darkest game of the series with the mask seducing the Skull Kid with pure evil and power before attempting to destroy the Earth by crashing the Moon into it. Such contrasting games.
Of course I also love the game play and the fact that the games are so huge and you can spend hours and hours working through them but at the end of the day I would say that I love the Zelda games because they are just such epic games that keep me playing for hours and keep me coming back for more and more and not many franchises can make me do that.