I just came across this theory. It suggests that Link and Zelda, in Ocarina of Time are siblings, probably twins. The evidence I have collected so far is how similar their models are, their age, how Impa teaches Link songs that are only meant for the royal family, the composer brothers commenting on how similar the two are, both having profetic dreams, and Link's mother having a horse (suggesting at least a high class).
I do have some reservations about this. There wasn't even a whisper of a long lost royal child. Also, while I can see Link abnegating royal titles in search of the glory he quested for, the shade never mentioned any such connection. His death armor definitely doesn't look royal. And, if he never did find out, there are quite a few people who would absolutely know, but are keeping it a secret.