Just to try and clarify the different Links and their ages...
The Link of the original "The Legend of Zelda" on the NES is supposed to be 10 years old. The game did not do a very good job of conveying that. I don't think it even tried. The official artwork for the game is a little bit goofy, and he looks more like a hobbit than a human of any particular age. Upon first finding out that Link was supposed to be 10 years old in the original Zelda, most people that I've seen seem surprised.
The Link of "Zelda II: Link's Adventure" on the NES is the same one as above, but at 16 years old. Sixteen seems to be seen as still a "kid" by Western standards, but it seems to be a popular "coming of age" point in Japan. In-game in Zelda II, Link looks about right for 16 year old, as he does in the artwork. I've talked to a couple of people who weren't even aware that there was a time gap in between Zelda 1&2. They just assumed that Zelda had been cursed in the ending of Zelda 1, and that they had forgotten it.
The Link of the animated cartoon shown in America appears to be the 16 year old version of the Link who starred in the original two games, except that he appears to be in some parallel world where Gannon didn't go after the Princess at the age of 10, so Link never defeated him at the age of 10, Zelda and Gannon retain their respective Triforces, and Link has never had the need to seek out his own Triforce.
The Link of "The Legend of Zelda: A Link to the Past" (set long before the original NES games) on the SNES is a new Link, who is apparently 16 years old, based on the official artwork, and the later-revealed fact that you can't wield the Master Sword until you're at least 16.
(The Link of the LTTP manga/comic which appeared in Nintendo Power around the time of the game's release is from LTTP (obviously), and while he looks young, he's much closer to sixteen than ten.)
The Link of "The Legend of Zelda: Link's Awakening" on the GameBoy is the same Link as above, with no significant time delay, meaning he's not much older than 16.
The Link of the CD-i Zelda games appears to be the same Link as above, based on the official artwork, but might not be, as they're definitely not considered "canon". He appears to be 16.
"The Legend of Zelda: Ocarina of Time" (set long before the SNES game) on the N64 was the first game to include both a "young" and an "adult" Link. The fully-apparent 10 year old version drew a great deal of confusion and uncomfortability from many at the time, but it was offset by the awsomeness of the game. Many people also found comfort in the fact that you could sometimes play as the 16 year old "adult" Link, who had been given a "mature" quality to him, beyond any of his 16 year old predecessors.
The Link of "Majora's Mask" on the N64 was the 10 year old version of the same Link as above, without the time travel aspect which gave birth to the 16 year old version.
The Link of the Capcom-developed "Oracle" games on the GBC has the same in-game sprite as the Link from Link's Awakening (which was the 16 year old LTTP Link), but that's just because the Oracle games were built off the Link's Awakening game engine. The official artwork shows him as being clearly younger than the Link's Awakening Link, and he is most likely 10 years old. This new Link is later revealed to be from the distant past of The Minish Cap, which is the distant past of the "Four Swords" games.
The Link of "The Wind Waker" on the GameCube is a new Link, 10 years old, now with the childish nature of the series exponentially increased through cel-shading. This caused a schism to explode within the Zelda fanbase, with "adult Link" being held up as the poster child of a side tired of putting up with the 10 year old version, and "original intent" being the rallying cry of the other side, due to the age of the Link in the original NES game.
Four Swords (on the GBA), Four Swords Adventures (on the GameCube), and The Minish Cap (on the GBA), all use official art in the style of the cel-shaded Wind Waker, despite not being cel-shaded, and feature in-game art that looks like a cross between A Link to the Past and The Wind Waker. They are all most likely 10 years old.
Although the bulk of Zelda games and popularity are seemingly revolving around the 16 year old version, Shigeru Miyamoto is apparently on the "10 year old" side of the fence. The return of "adult Link" in Twilight Princess (technically an older version of the cel-shaded Wind Waker Link) seems to be a concession.
I personally wish there wasn't a fence.
Edit: Fixed some mess.