Link and Zelda are so special to me. It goes beyond calling them a romantic couple (ie. "ZeLink"). Their bond is so strong and everlasting, even outside of the fact that they're fated to be eternally reincarnated together. Saying they're a romantic couple just removes the complexity and deepness of their relationship, in my opinion.
I have this headcanon for them that I really like. I think part of the reason they're so close is that they both experienced a significant loss as very young children.
We never really see Link's mother, and we don't see Zelda's mother or father. Why is that? I think it's because they're dead. Call it stereotypical, but follow me here as I explain my headcanon further:
Link's mother died when Link was he was very, very young - probably 2 or 3 years old. He can't remember her face or her voice, and that really bothers him. His father tells him how much his mother loved him and how excited she was when she found out she was pregnant, as well as when he was born. She took such good care of him and just wanted him to grow into a strong, kind person.
Link has dreams where his mother is standing in front of him, and he tries to run to her and touch her, even if it's just for a moment - but she always disappears right as he reaches her. He wakes up crying from those.
Zelda's mother and father died when she was 8 years old. They died at the same time while they were away on a trip. Courtesy of my friend Nikki, I like the idea that Zelda had prophetic dreams about her parents' death but couldn't fully understand what they were at the time. She just woke up scared and went to her parents' side whenever they happened.
Even now, she feels like it's partially her fault for not preventing their deaths. She tends to blame herself for a lot of things, as I've probably discussed elsewhere on this website (and if I haven't, PLEASE email me and kick me to do it).
When Zelda's parents died, Link was the one person she could actually speak to. Everyone else was a scary, cruel adult who kept trying to tell her to calm down and accept what happened. Link was already familiar to her and actually let her get her emotions out. When she couldn't cry anymore, he made a promise to her right there, and she did the same: they were going to help each other grow into their best selves so that their parents would be proud watching them from the afterlife, and they would support each other if they had their own children (regardless of who the other parents are) so that they could be around for as long as possible, ensuring their children wouldn't have to experience the loss of a parent like they did.
They made a promise, and they've kept it ever since. They have dedicated their lives to themselves and each other. It is a form of true love that trascends any traditional idea of romantic love, familial love, or platonic love. I know it's just a headcanon, but it means a lot to me. I love these two so much. I could go on and on about them just from what we see in canon, but I think it's fun to imagine their dynamic outside of what we're shown, too.