The Legend of Zelda series is always about the same basic thing; a young boy, Link is called upon to accomplish a quest that his name sake, the great hero of Hyrule (at some unspecified time in the past) undertook. Said quest usually involves being tossed randomly into a situation of battle (often times as a young child) only to meet the princess of the realm, Zelda and uncover a plot by Ganondorf to take over and destroy the realm by getting his hands on the Triforce, an ancient remnant of Hyrule's Goddesses. Link always kicks enormous amounts of ass and becomes the great hero of the realm. The story's usually the same, with whatever goofy humor Miyamoto decides to throw in there and the few variations of gameplay.
And the gameplay is the key to all the Zelda games. The famous dungeons, usually 7-10 of them throughout the game, are notoriously well crafted, difficult without being impossible and almost always incredible beautiful. The time and energy put into the Zelda games usually produces lavish, monstrous games that rewrite how the genre is played. And that is why it's the greatest franchise of all time.
It's impossible to build a chronology for the games, as they are never specifically linked, but there are a variety of little details that give out some information as to how these break down.
The Legend of Zelda, released in 1986 for the NES, created and established the dungeon actioner genre and introduced us to the cast of now well known characters. The story involves Link being called upon to defeat Ganon, already in his pig form, after retrieving the triforce pieces that Zelda scattered throughout the land.
Zelda II: The Adventures of Link was released the next year and involves the same Link only a few months later. It's considered by most to be at the end of the chronology as it is never referenced in other games. Moreover it gives cause for all of the princesses being named Zelda. A Zelda of many generations before was put to sleep for her transgressions against the King by hiding the triforce, so the prince decreed that all princesses of the realm would carry the name Zelda.
The Legend of Zelda: A Link to the Past was released for the SNES in 1991, making the great leap to 16 bit, the only game from the sequence to appear on the console. This game occurs earlier in the Zelda chronology, revolving around Link's first attempt to retrieve the Master sword and defeat Ganon, still in pig form. It also makes first reference to the origins of Ganon, that is Ganondorf the thief, who stole the triforce and attempted to overtake Hyrule, and the Seven Sages who seal of the Golden Land from him.
With most of the Zelda games, shortly after a main sequence game, a spin off or sequel, something lighter is released not involving Ganon. In 1993, Link's Awakening was released for the Gameboy as just that, a quest for enlightenment after defeating Ganon.
It wasn't until 1998 that the next true Zelda game was released, and boy was it a game. The Legend of Zelda: Ocarina of Time is considered by many as the greatest video game ever made. I tend to agree. Chronologically, it's the first in the series, taking place when Ganondorf is still human, a thief from the desert in the west. He steals the triforce, which shortly after breaks apart because of his impure intentions. Link's quest involves finding and putting the triforce back together and enacting all of the seven sage's seals. This game more or less invented the genre as we know it today. Autojumps, aiming, analog controls, fully 3D environments, and the sheer scope of the game make it a classic without peer.
Majora's Mask does the whole side story thing again. It's about Link's return to youth after the events of Ocarina, in which he's robbed and drafted to help stop the moon from destroying another world.
Wind Waker, released for the Gamecube in 2003, takes place hundreds of years after Ocarina, after the land of Hyrule has been destroyed and is underwater. We meet Ganon as a pig once more, and discover that Link and Zelda are both reincarnations of their Ocarina counterparts. This game took a sharp turn from previous games, still extremely well made, but alienating many fans, with it's cel shaded graphics and fetch quests. The game took as long as any previous Zelda to complete, but half of that time was spent sailing from island to island, floating around the great Hyrule sea. It could be....frustrating at times.
And that brings us to the newest entry, the big Wii release game, Twilight Princess. The newest Zelda takes place a few decades after the Ocarina of Time, this time our Link is an adult, living on his own in southern village as a wrangler. It's the darkest and most mature of the Zelda games and along with its Wii controls, it manages to be the most breathtakingly cinematic of the games as well. Ganon first appears as pig, but reverts to Ganondorf at the end. Easily the longest of the Zelda games, Twilight Princess introduces tons of new elements, not the least of which is the chance to play as a wolf various times throughout.
The Legend of Zelda series is a long running Nintendo tradition, the kind that will never fade away, if only because of the fierce loyalty of its fans. These games are masterpieces, every one and never once has Nintendo let its fans down. We'll just go ahead and pretend The CDi games never existed (they weren't Nintendo anyways).