Author: Maryh
NOTE: In this essay, I will refer to the four founders of Hogwarts by first name, to distinguish them from houses that bear their last names.
In the books, Slytherin house is associated with an obsession with pure bloodlines. I don't think that is an essential characteristic of Slytherin house, nor that it is necessarily a long-standing one.
Did Salazar Slytherin care about blood purity? Actually, the only thing we know from reliable historical sources is that he didn't want children of muggle parents to come to Hogwarts, because he thought they were untrustworthy. Considering that witches and wizards were being persecuted at the time, so much so that it was deemed necessary to keep the existence of Hogwarts secret from muggles, letting muggle-born wizards and witches attend Hogwarts was a clear security risk.
We also know that Salazar broke with Godric Gryffindor over this matter, despite the fact that according to the sorting hat (OotP) they were very good friends:
"For were there such friends anywhere
As Slytherin and Gryffindor?"
What happened?
There is a marked difference between the ways Gryffindors and Slytherins approach danger and risks. Gryffindors tend to underestimate danger, and are much more prone to take risks. Slytherins tend to overestimate danger (after all, as far as we know, muggle-borns never did betray Hogwarts to other muggles), and will not take risks without a clear need. Salazar was not willing to risk Hogwarts to muggle-borns -- Godric was.
In the same sorting hat song from OotP referenced above, the sorting hat also says:
"Said Slytherin, We'll teach just those
Whose ancestry is purest."
and
"For instance, Slytherin
Took only pure-blood wizards
Of great cunning, just like him,"
Nevertheless, the Sorting Hat has no problem putting people who are not pure-blooded in Slytherin. And the sorting hat mentions pure-blood as a Slytherin criterion only in this this song. The one criterion that is always mentioned by the sorting hat is cunning ("shrewd"). The other, mentioned almost as often, is ambition ("way to greatness", "power-hungry").
So how did all this get mixed up with blood-lines?
Initially, Salazar would have wanted students whose ancestry was purest, who were pureblood like him, because they would constitute the lowest security risk to Hogwarts. Remember, he is likely to overestimate the danger rather than underestimate it, and would want to reduce the risks to Hogwarts and himself.
Fast forward to the time of Voldemort. The wizarding world has had hundreds of years of practical experience keeping themselves hidden from Muggles. And in the last couple of hundred years, things have changed such that European and British muggles no longer believe in magic. Now, even if a muggle sees magic, he likely won't recognize it as such, nor will he be believed if he tries to tell anyone else about it. In fact, the Wizarding world counts on this new attitude of muggles to the extent that they don't worry that telling the Prime Minister of Britain about their existence might compromise their hiddenness to the Muggle world. Clearly, modern wizards are not worried about muggle-born wizards and witches betraying the secret of their existence to the Muggle world.
And yet, it is still part of history that Salazar Slytherin broke with his great friend, Godric Gryffindor, over the question of allowing muggle-borns to attend Hogwarts. How would a modern day witch or wizard understand that? One who had never experienced the persecution of wizarding folk by muggles, and who had never feared them? And one who had been taught Magical History by the excruciatingly boring Professor Binns? The obvious interpretation would be that Salazar thought that pureblood wizards and witches were inherently better than the muggle-born.
We don't know exactly how this has played out over the years. It is quite possible that after a couple of hundred years of experience hiding from muggles, the Slytherins lost their fear of muggle-borns, and had no trouble accepting cunning, ambitious muggle-borns to the house. It would be clear to Slytherins that muggle-borns could be just as powerful and ambitious, as it would be clear to Ravenclaws that they could be as intelligent, and to Gryffindors that they could be as brave. In fact, it is the Hufflepuff house that would seem to be most likely to stand on the importance of bloodlines for their own sake.
Of all the houses, it is the Hufflepuffs that care most about rules. And in PS/SS, the sorting hat calls them "loyal" and "true". But who are Hufflepuffs loyal and true to? I can very well imagine that at some point Hufflepuffs might have thought loyalty applied only to "real" wizards and witches, defined as those of pure blood. The Gryffindors and Ravenclaws would have been unlikely to be taken in by this idea. But some cunning, ambitious Slytherins of pure blood may very well have used the idea to their advantage.
Even if the idea of preferring pureblood wizards for their ancestry alone may have been started or promoted initially by Hufflepuff, there would still have been a tension between that and the other Hufflepuff ideals of hard work and justice. And it would be easier to identify the people to whom one should be loyal as "all wizards and witches" rather than just those of pure blood. In modern times, it has been the ambitious pureblood Slytherins who have raised the banner of the pureblood for their own ends, easily twisting the real reason Salazar did not want to bring muggle-borns to Hogwarts.
Clearly, that is what Voldemort did.
I highly recommend the essay "In Defense of Salazar Slytherin" by Russ Griffin which can be found at: Slytherin.doc. He makes an excellent case that Salazar's objection to muggle-borns was based on security issues rather than bigotry, and also addresses the Chamber of Secrets and the basilisk.