Originally the game is hinting that Link and Saria want to be more than just friends. It is heavily implied that Saria is the main love interest of our hero. She cares for him more than other Kokiri's, she's always happy to see him and always happy for him, and despite not wanting him to leave, sends Link off with a gift and a smile. These are all cliche (though very mature) female love interest things to do. However, the reason the LinkxZelda seems more concrete to people is that when Saria turns into a sage, Navi says "Saria will always be... your friend." That ellipsis is crucial, saying that she could've been something more, but now can never be. The thought of the LinkxSaria relationship is pretty much gone after that moment even though eventually Link goes back in time to a point where Saria never becomes a sage. That moment was made to banish the thought of LinkxSaria from your head. If you notice, not much more happens with Saria after this point passes. The possibility of LinkxZelda, however, continues until the end of the game and even past. Really, as a love interest, it doesn't seem like the game is pairing up Link and Zelda but just giving Zelda that atmosphere of "anybody could fall in love with her." It's Link's desperate attempts to save Zelda (with her being a princess and all) that a spark even flies between these two, but that doesn't necessarily mean they will wind up together. At the end of the game, the relationship seems more real as the princess and her knight work together to overcome their foe. Again we see cliche pairings as the brave knight generally ends up with the fair maiden. Here, Link and Zelda now must do what Link and Saria had to do, in that they must say goodbye and admit that they can never be a couple. The difference between this relationship, however, is that when Link goes back in time, he returns to Zelda... not Saria, but Zelda. There's seems to be this "needing" in Link to be there. Now eventually we know that Link warns of what will happen with Ganondorf and yadda yadda yadda, but when you saw that ending scene for the first time, is that really what came to mind? The ending scene was really pushing forward the destiny aspect that Link and Zelda belong together (not necessarily romantically, just that they belonged in each others' lives). And a relationship like that would stereotypically lead to romance. Even after OoT, in Majora's Mask, Link has memories of Zelda as he departs from Hyrule, again showing his special bond to this girl. The Legend of Zelda in itself is essentially how destiny winds up forcing these two important beings to find their way into each others' lives.
Nintendo wanted to show that Link's main love interest at the beginning of OoT was indeed Saria, but they then set the tables so that destiny would bring Zelda closer to the boy's heart.