In Ocarina of Time it does not say that both Link's parents died, just that his motherwas injured while she was caught in a big battle, then died as she left him with the Deku Tree. There was never any mention of his father, and did you ever hear of a Queen of Hyrule in the game.
In Zelda: A Link to the Past you are raised by your uncle, and after he leaves in the beginning of the game and you hear Zelda's telepathic plead for your assistance, when you first go into the castle and find your uncle, he says, "Link take my sword and shield, you must save the Princess she is your ........" It was a really long time since I've played and beaten the game, but I'm pretty sure I remember the game saying they were brother and sister at the end of the game. Link's hair does vary in color throughout the games from blond to reddish, where Zelda is always blond. and in Link to the past, all the other princesses were not blond. And the instruction booklet in the original NES zelda it specifically says, "You must save your sister from Ganon."
The Mario games always feature the same Mario and Luigi and Princess Toadstool and Bowser, but as far as I've been able to see, the Zelda games are different in that each games protagonist Link is either a descendant or a ancestor of the protagonist link of the previous installment (except for Ocarina of Time and Majora's Mask, which were directly related). In effect, each Link and Zelda are different Links and Zeldas from other games, although Ganondorf is always the same force that the original Ganondorf had become, whenever that was. Link could have been more related to Zelda at one point in history then another. Both of them hold different parts of the Triforce as well, so they would need to be separated in order to keep the power safe.
Personally, I don't think so. And to the above people, Zelda was brunette(Probably misspelled that) in A Link To The Past, Twilight Princess, and Zelda 1 & Zelda 2. And as for the instruction booklet, thats pretty outdated. Instructions aren't known for being extremely accurate. Zola, anybody?
Also, every link is a reincarnation, not a descendant (explained at the end of skyward sword). If you played the wind waker, the king of red lions (actually the king of hyrule, zelda's dad) said to jabun that the current link had no connection to the one from oot.
To answer the question, it is never confirmed whether and incarnation of Link and Zelda are actually related. And in the original NES A Link to the Past's manual. It probably is referring to Zelda as Link's sister. But manuals have mistranslated before. One great example is in the Sonic series for the game Sonic CD, they named the girl you rescue, by the name of Sally Acorn, although it is obvious that the character you're supposed to rescue is actually Amy Rose/Rosy the Rascal. And correct me if I'm wrong, but didn't they remove your Uncle's line: "You must save the Princess, she is your....." in the GBA version? I believe they removed that line...And only had him say that you must take his sword and sheild and taught you how to use the Spin Attack, then fainted. It is possible that a handful of them are related though. All the Zeldas are related to each other, that is obvious, since they all share the blood of the Goddess and the Royal Line. So far it's only confirmed that two incarnations of Link are related by blood: The Hero of Time and the Hero Chosen by the Gods (OoT/MM and TP Link). And for anyone that is asking there are at the most, about 10 incarnations of Link across the series and about 11 or 12 incarnations of Zelda.19:31, February 12, 2013 (UTC)