Princess Zelda is the eponymous character of the Legend of Zelda series. She is best known for getting kidnapped, never kissing Link, and having the entire series named after her even though you rarely see her in any of the games.
Princess Zelda came along in a time when princesses were only good at two things: Attracting bad guys to kidnap them, and attracting heroes to save them. And being attractive. Princess Zelda was originally conceived by Shigeru Miyamoto; God of Video Games, and was inspired by a woman named Zelda Fitzgerald; wife of some author dude none of us have heard of.
Left to Right: Princess Zelda, someone who is not Princess Zelda.
In all honestly, Zelda Fitzgerald was an awesome woman, but you'll have to look up another topic on her.
Zelda may have had a rocky start in 1986, but her first major break was in 1989 when she starred in a tv cartoon series bearing her name. While she is still occasionally saved by Link in the series, she spends most of her time fighting with Link.
Well excuuuuuuuuuse me, bitch.
As the 90s progressed, Zelda decided to go the opposite path of her co-worker Princess Peach. Instead of sticking to the traditional helpless brain damaged role that women had been locked in until the late 1900s, Zelda seemed to channel the spirit of Fitzgerald (ok seriously, look that woman up. She had some kickass quotes and shit) and turn more and more independent.
Apart from being able to cast some seriously cool magic shit, Princess Zelda is also the first and currently only princess to ever have been both a ninja and a pirate.
Sadly, she never wore this t-shirt.
It also doesn't hurt your reputation as a badass princess that most of the time, the only person able to kidnap you has been repeatedly called the very definition of badass.
Above: The most badass ginger ever. Of all time.
Princess Zelda also has the Triforce of Wisdom; a relic that grants a wish when brought together with the Triforce of Courage and the Triforce of Power. This wish has allegedly been made by Ganondorf more than once, yet it is still the main reason Ganondorf kidnaps Zelda. That or he's just fucking with us, the dick.
Zelda doesn't always play a major part in Zelda games; sometimes she doesn't play a part at all. Below is a brief reference of Zelda's contribution to each game with her name on it.
WARNING: Expect spoilers up the wazzoo.
The Legend of Zelda (1987): Princess Zelda is kidnapped by Ganon. She also breaks the Triforce of Wisdom into a shit-ton of pieces and you have to collect them all before you get to save her. This is never really explained.
Zelda II: The Adventure of Link (1988): Zelda has been put to sleep in some kind of inheritance dispute involving her dick brother and some wizard. She basically rips off Sleeping Beauty.
The Legend of Zelda: A Link to the Past (1992): Zelda gets kidnapped by a wizard. Link saves her, and puts her in a church for safe keeping while he goes to kick the wizard's ass. After he does so, Zelda gets kidnapped by Ganon. You can see a pattern sort of developing here.
The Legend of Zelda: Link's Awakening (1993): She isn't even in this game. What the fuck?
The Legend of Zelda: Ocarina of Time (1998): Zelda actually manages to go a record length of time without being kidnapped. After you break into her castle and show her your jewels, she does what you would expect her to; say she saw them in a dream and befriends you. After collecting some more jewels and getting married to a fish, Link comes back to Zelda only to catch her getting the fuck out of Hyrule Castle like a Thai prostitute out of the trunk of a Honda civic. She doesn't show up again until seven years later when she becomes a ninja and trains Link in the art of music. Then she gets kidnapped by Ganondorf.
The Legend of Zelda: Majora's Mask (2000): She gives Link the Ocarina of Time in a flashback. She also comes on to him.
The Legend of Zelda: Oracle of Seasons/Ages (2001): She only makes an appearance if you beat one game and put your code into the other and beat it. In a humbling blow, she gets kidnapped by Ganondorf's mom, who wants to sacrifice her to bring back Ganondorf.
The Legend of Zelda: The Wind Waker (2003): In her pirate debut, Zelda is introduced in the first 20 minutes of gameplay. While she almost gets kidnapped by Ganondorf's bird, Link's sister gets kidnapped instead. They go sailing to fetch her, and Link ends up getting his ass kicked by the bird. Zelda doesn't really show up until later on when they raid an island that Link happens to be on, and one of the pirates imply she should get knocked up by one of the other pirates. She blows it off as a harmless joke (my co-workers aren't as sassy). She spots Link spying on them, so she sets him up so that he can knick some bombs from them while they get tanked. They don't meet again until Link gets the master sword, faces Ganondorf, gets his ass kicked, and then gets saved by Zelda. They then go to the bottom of the ocean in old Hyrule where they find out Zelda isn't a pirate, but really Princess Zelda. Given her track record of kicking ass and forgetting names, they decide they should hide her there, at the bottom of the fucking ocean, for safe keeping. No combo breakers here. On the plus side, she helps you fight Ganondorf in one of the most awesome final boss fights ever.
The Legend of Zelda: Four Swords Adventures (2004): Fuck this game. Zelda gets kidnapped in it, and that's pretty much the only recognizable part of the story.
The Legend of Zelda: The Minish Cap (2005): Zelda and Link are actually close friends in this one right off the bat. They go frolicking to the fair, and have a gay ol' time. Then some purple dude named Vaati turns her into stone. She remains stoned for the vast majority of the game.
The Legend of Zelda: Twilight Princess (2006): For the first time, Zelda starts acting like a real life princess and does diplomatic shit like running a kingdom. She gets invaded by some dark wizard and forced to surrender. However, this is where the Progressive Princessism ends and Traditional Princessism returns. She is held captive in a tower for the whole game. Around the end though, she gets possessed and fights you, then she rides shotgun (or Bow of Light) on Epona with Link in the final battle. Also worth noting is that she is allegedly 4 years older than Link in this game.
The Legend of Zelda: Phantom Hourglass (2007): Pirate Zelda returns, but this time she manages to get kidnapped before your very eyes long before you get a chance to move Link around. She boards a phantom pirate ship, and it takes off with her. During her voyage on said ship, she is turned to stone. Once again, she remains stoned for the duration of the game.
The Legend of Zelda: Spirit Tracks (2009): Princess Zelda gets a record amount of screen-time due to the fact that she has taken over Navi's role in the the most recent instalment of her games. The fun twist in this story is that while she gets to hang with Link most of the game, she still spends most of the game kidnapped. This is due to the fact that early on in the game, she got bitch-smacked so hard that she fell out of her body. The bad guys then made off with her body, leaving her less male-friendly side with Link.
Honorable Mention; Super Smash Bros. series (2001, 2008): Zelda first made her appearance in the GameCube's take on how Nintendo characters spend their free time between games in 2001. While there is absolutely no storyline going on here, the real reason why it is worth mentioning is the fact that in these games, Zelda can beat the life-loving stupid out of Princess Peach. The series is also the only other place her ninja form Sheik makes an ass-kicking appearance.