First of all, let's take note that the term Hylian, along with most of Zelda's "mythology" was established in ALttP. What's most interesting however is that according to ALttP, Hylians no longer exist!
"The legends say the mythical gods of Hyrule had as their chosen people the Hylia. These ancient people left scrolls that are the primary source of the legends."
"With their magic infused blood, the Hylian people were endowed with psychic powers and skill in wizardry. It was also said that their long, pointed ears enabled them to hear special messages from the gods, so they were held in high esteem by many people in Hyrule. Their descendants settled in various parts of the world and passed on their knowledge and magical lore to all people. But in its passing, the lore was often distorted or lost altogether.
In Hyrule, there are many Hylian buildings which are mentioned repeatedly in the legends. These buildings, which now lie in ruin, pale shadows of their former splendor, are closely tied to the Triforce."
This passage here by the way ("With their magic infused blood, the Hylian people were endowed with psychic powers and skill in wizardry.") is why I keep saying Hylians should have mages!
Anyway, as you can see, ALttP treats Hylians as bygones ("they
were held in high esteem by many people in Hyrule. Their descendants settled in various parts of the world and passed on their knowledge and magical lore to all people. But in its passing, the lore was often distorted or lost altogether.")
Yet, every single person in ALttP has pointy ears! How does that work? Well, it's really quite simple, the people in ALttP are the descendants that the above passage speaks of, whose blood however has been mixed over the generations with that of non-Hylians to the point that pure-blood Hylians do not exist anymore.
Or even if they exist (and they probably do, because an entire race doesn't disappear that easily), they have lost their cultural identity and no longer identify themselves as Hylians (consider ancient Romans and Italians).
I like to call these half breed descendants Hyrulians, and use the word Hyrulean instead for anything and anybody that comes from Hyrule. But that's just me.
Conversely, in OoT which happens many centuries before ALttP, the Hylians are alive and very aware of their identity:
"They say we [COLOR=sky blue]Hylians [/COLOR]have big ears
in order to hear the voices of the
gods...but I've never heard them!"
Some think the pure blood Hylians have ears slightly different from the half breed descendants, that pure Hylian ears point outward
while the half breed descendants have ears pointing upward
but that might just be due to a different art style, hard to tell.
So can it be said that Hylians stopped existing because they mixed their blood with humans?
Well... not quite.
The thing is, Hylians
are humans. Always have been. They are, in fact, a race of humans, much like, say, caucasians.
And really, this is pretty much necessary for Hylians to reproduce with non-Hylian humans. See that's actually what scientifically differentiates species from race. Members of the same species but of different races can have off-springs together, whereas members of different species cannot (human+monkey... not gonna work).
And if you check out those quotes I dug up for you, you'll see that Hylians are not alone in being considered humans:
"Ganon... This beast was once
of the Gerudo... Once human.
He was called Ganondorf!"
Yup, the Gerudo tribe is a race of humans as well! (Can't bring up any evidence but I imagine so are the Sheikah... assuming they are not just a Hylian sub-tribe, as I suspect they might be. And may as well lump the Wind Tribe in there too)
On the other hand, Gorons and Zoras are
clearly not considered humans.
Again, observe the quotes above:
"Goron or human,
health is all
that matters!"
"Well, this isn't good. A human
doctor won't do, huh...
That old coot reminded me,
though... I've heard of a shaman in
Kakariko Village, in the Eldin lands,
who's tended Gorons and Zoras."
"And what's with putting that temple
so deep that humans can't swim
there?! I swear, those Zoras..."
"He is a proud Goron, and he can
be...touchy. If he knew he had
been saved by a human..."
...which incidentally means Hylians and Zoras can't reproduce together... not much of a shock considering they are mammal and oviparous respectively