Hyrule Warriors

Link (or least that it's implied that he) cries when Zelda sealed herself. Zelda apologizes for testing Link, and it wrenched her heart that she (as Hylia of course) planned to use Link in such a way. This is a very powerful display of emotions to display for even the closest of friends.

The fact that so many fans cannot possibly conceive having a such a strong connection could not exist without it being sexually driven is frightfully sad.
Seriously, I can smell the fedoras from here.

Zelda II : The Adventure of Link, where the curtains close and Zelda kisses Link.
Link's dreaming in Link's Awakening, when he calls Marin Zelda.
Link + Tetra
Link + Zelda in Spirit Tracks


I don't remember if there was anything, but there may have been a slight sign of traction in A Link Between Worlds as well.

Re: AoL - There's a lot in presuming a kiss given as a reward means anything but "thank you".
Re: Link's Awakening - Yeah, he called Marin 'Zelda' because she looked just like Zelda because she looked just like Zelda. How is that a sign of tension?

You just gave their names in the last two 'examples', so I'm not sure why you think either of those demonstrated a deeper physical attraction.

Yes, Link saves Zelda a lot, but his motivation for doing so is generally more significant than "get the girl". In fact, AoL and Phantom Hourglass were the only times Zelda is the actual endgame. In the latter, this is because he actually spent an entire game before and sometime sense actually being around her. I mean, if one of my only friends in the world were kidnapped by a nightmare boat, I would like to think I'd go to save her.
In AoL, Zelda is someone who he's never met before and he only tries to save her because some old lady tells him it's his destiny or whatever.

TL;DR version: Link could gender swap in most games without much awkwardness or possible controversy. Yes, there would be some minute same-sex flirting, but there's nothing to actually be called "romance" in the series (at least none involving Link).