Well, firstly, Link does have parents. We simply are not shown them due to circumstances within the story (he had to come from somewhere). The technical reason is simply because Nintendo chose to write it that way, but it certainly does have an effect open the psychology of the game itself. Link, as Ghirahim said, is a mysterious character. Giving him an obvious origin would take away from the cloud over Link's past. He also represents childish innocence coming into a much darker world, and giving him to adult role models would take away from the dramatic curve of his growing up. His direct mother or father (though mentioned at times) logically do not appear in Ocarina of Time. Remember that an important aspect of the early story is that Link doesn't have a fairy. We also find that he matures after seven years, which comes as an initial shock to the player, as the Kokiri are not supposed to ever take on adult forms. This is because he is really Hylian, delivered to the Kokiri by his dying mother. If he knew of his parents, then he would also know that he is not Kokiri, thus he would assume himself Hylian and the sense of "the boy who never really fit in" would be entirely lost.
Another possible reason is, quite simply, because he is simply destined to become a great hero. Not only would having a close family interfere with his quest, the concept is tradition. Think of the countless epic tales we hear of, no matter how old. How many of them had constant contact with their parents early in life? There is something to be said for childhood seclusion when it comes to heroes. It creates a much better mood.
Finally, having parents would alter the atmosphere in the game. Imagine how differently you feel when you play, say, Pokemon, and you know you have a parent back in whatever town you depart from ready to aid and support you. It is certainly a different "mentality" then Ocarina of Time, when you feel that (save for a slight amount of support from allies) you are entirely alone. Throughout the course of Wind Waker, we felt slightly more comfortable out at sea knowing that our Grandmother would be waiting to provide us with her soup (not coincidentally the most powerful potion in the game). It all depends upon the mood that the developers desire to provide.
Would I like to see Link's parents appear in the world? I suppose so, though I feel it would take away from the game itself.