I created an account just to respond and weigh in with my opinion. So, hopefully, I am not out of turn and responding to this forum when the last response was 2 years ago won't get me in trouble with moderators and administrators.
So here goes: I believe that Link is reincarnated throughout his various incarnations in The Legend of Zelda series. Furthermore, and to clarify, I believe that the reincarnated Link is SS Link (Skyward Sword). In Skyward Sword, Zelda aka Hylia calls Link the Chosen Hero, meaning that SS Link is Hylia's Chosen Hero, this is important to remember as the Light Spirit in Twilight Princess, Ordona reveals to TP Link that The Spirit of the Hero resided within TP Link's veins, and lay dormant all this time, Ordona refers to The Spirit of The Hero as being the power of the hero, that his is the one true power that slept inside him. This implies a literal component to The Spirit of the Hero, not a metamorphical one as others have all been saying. I believe that Ordona was referring to SS Link when referring to "his", and "the spirit of the hero", meaning that a metaphysical component of SS Link survived his physical death, and was reincarnated into TP Link. Beyond the canon lore provided to us, I also believe in the reincarnation theory for one simple reason, Link's fighting prowess. Think about it, can you recall the various times in LoZ where characters have all praised Link's affinity with the sword? They all agree that Link is a natural, talented and competent swordsman, and furthermore, while everyone would say that this is merely gameplay convenience, this doesn't explain why characters all compliment Link's quick learning and natural talent for swordsmanship. The obvious answer to this is reincarnation, every Link is SS Link reincarnated, this doesn't mean that every incarnation of Link is not a unique being with their own thoughts and memories, they are, it merely means that a component of SS Link (The Spirit of The Hero) survives his biological or physical death, and is thus reborn into a new vessel or body. Link's natural combat skills are clearly the signs of centuries of experience, his skill with the sword is seemingly unrivaled because it has become second nature to him. It also explains why The Master Sword accepts each incarnation of Link as its Master, because Fi, who sleeps within the Master Sword recognizes The Spirit of The Hero as being a component of SS Link, and although this new Hero does not share SS Link's thoughts and memories, they do share his spirit and his valor, because it is his. This also means that the Zelda Universe also shows that mind-body dualism is real, mind-body dualism is a theory in philosophy which posits that there is a metaphysical component to one's existence. I'm actually seriously considering writing an essay on this topic, that being, Link is a product of reincarnation and I will set out to persuade readers of this thesis by using three games in the series: Skyward Sword, Ocarina of Time, and Twilight Princess. I will also utilize reincarnation and mind-body dualism, so there will be quite a bit of philosophy to my essay.
I hope everyone found my explanation reasonable, and if anyone has any counter-arguments, feel free to reply, or send me a private message, as I am eager to have a polite debate about this topic.