Apologies ahead of time if there is already a topic about this, but I failed to find an active one.
For years there has been the theory that Link and Zelda are in fact brother and sister. A big part of the controversy stems from a quote in Link To The Past:
"Zelda is your..."
It is thought the unfinished sentence was refering to them being siblings.
Others also believe there is a familial relationship between the two because of them having the same hair and eye colors.
I personally don't believe this theory is true. My reasoning:
1) The 2002 release of Link To The Past reworded the previously mentioned quote to "It is your destiny to save Zelda." It was not meant to say anything about her being Link's sister.
2) In Ocarina Of Time, we learn that Link's mother fled during wartime, taking baby Link with her. If Link and Zelda were indeed siblings, and their mother the queen, her fleeing to the forest makes no sense. What sense does it make for a queen to flee into the middle of Hyrule Field during a battle? Also, why did she take only Link? What about Zelda?
3) It's no argument to say they have the same hair and eye colors. There are plenty of people in the world with the same hair and eye color, yet they are not related.