For all of the Links and Zeldas who have teamed up to fight Ganon and his minions throughout the history of Hyrule (not to mention alternate timelines), it's interesting that I don't think any of them ever got together romantically. There's apparently even been some online speculation that Link might be gay, although I don't know that he's shown interest in any males either. With this in mind, it's interesting that DiC's Zelda cartoon, made when there was only one game out , really played up the sexual tension between the hero and the princess. The cartoon was part of the Super Mario Bros. Super Show, aired on Fridays in lieu of a Mario cartoon. It appears to be a not uncommon opinion on the Internet that the Zelda cartoons were better than the Mario ones, and I will admit that they apparently took slightly more care with the Zelda episodes (although still not THAT much, since it WAS a DiC production, after all). In the show, Link was constantly hitting on Zelda in the most obnoxious ways possible, and there were occasional hints (especially in the episode "The Missing Link") that the princess secretly returned his affections but didn't want him to know. Another recurring character was Spryte, a fairy who had a crush on Link despite being much, much smaller than him.  It's Peter Pan and Tinker Bell all over again, I suppose. I guess it's Link's fault for dressing in that green outfit. And, of course, Ganon was there, and he was very hands-on in this take. He was always showing up in person to steal the Triforce of Wisdom, and insisting that nothing could stop him when he had both Triforces together, even though someone always did. I believe most of the monsters from the first game showed up at some point or other, but they were all morons. One odd rule on the show was that the monsters never actually died, but simply regenerated back in Ganon's Evil Jar, a fixture of his underworld throne room where he kept his henchmen when he didn't need them. They always were reluctant to imply actual death in cartoons of the era, so perhaps that was their way of avoiding it, but I suppose that regeneration kind of makes sense for video game characters anyway.
As with most shows, especially ones aimed at kids, there was never any real continuity. There was always some lame excuse for why Link and Zelda didn't just take the Triforce of Power that Ganon left out in the open. And of course the two heroes never got together; I suspect people would have complained of the show jumping the Zora if they had. When they appeared in a few Captain N episodes, however, they no longer bickered all the time, and Zelda did occasionally kiss Link. So their relationship presumably progressed at least slightly, albeit not on screen.
If anyone wants me to review individual episodes of the cartoon, let me know. I also still have the Super Mario World series to get through, if anyone cares. And if you DON'T care, well, EXCUSE me, Princess! 
 Actually, Zelda II was released in Japan in 1987 and in North America in 1988, while the cartoon aired in 1989. I don't think it makes any references to the second game, however (for instance, there are only two Triforces in the show, while the game brought in a third), so the writers presumably hadn't played it.
 Maybe someone should write fanfic in which Spryte hooks up with the Big Goron. Now THERE'S a size difference!
 Yeah, I had to work that in somewhere.