A few titles have direct sequels but for the most part the whole series has the games taking so far apart that little is retained from a narrative point of view.
Link's Awakening is a direct sequel to A Link to the Past
Majora's Mask is a direct sequel to Ocarina of Time
Phantom Hourglass is a direct sequel to Wind Waker
Even then all the games don't really carry over anything from each other or if they do they are good about giving you a quick prologue to update you. Like Final Fantasy the series is designs in a way to make ever new entry newbie friendly. There is a giant myth arc that incorporates the whole franchise but it has little to do with the stories and mostly serves as talking points for fans.