Warning, spoilers may follow:
First of all, I think we have to discount anything that comes out of the Watcher’s Council. They regularly manipulate and lie to the Slayers. It certainly would not be above them to lie about the nature of vampires if it made the Slayer easier to control.
Second, there is some evidence that, when a person is turned into a vampire, their soul doesn’t completely vanish. Look at the Judge from season two. He’s supposedly is able to sense the “good” in people and burn it out of them. His first victim? A vampire. He also indicates that he could do the same to Spike, but doesn’t out of some form of gratitude for being reassembled. Now, “good” and “soul” are not necessarily synonymous, but it is telling that the way Joss tells us that Angel has lost his soul is by having the Judge be unable to destroy him.
I think what this means is that when someone is turned into a vampire, sometimes a reminant of a soul is left behind. How much seems to be random, or based on some unknown factor (it might even be a defect peculiar to vampires descended from Drucilla, who, as a schizophrenic psychic, is probably fairly unique in vampirdom) Normally, this has little to no effect on the vampire, who is dominated by the impulses of the demon spirit. In Spike, however, the demon is restrained by the chip, allowing the flicker of a soul that was left in him some measure of control. Hence, Spike’s gravitation towards the Scoobies and eventual infatuation with Buffy, his protectivness towards Dawn, and his respect for Joyce. Oh, and his help in the prevention of at least three apocalypses.
Now, this isn’t to say that there are two “people” in one body, Spike the vampire and William the human. I don’t think that’s even true for Angel. I think the Angel/Angelus split personality thing is a rationalization on Angel’s behalf, a way of distancing himself from his actions when he was without a soul. It certainly never came up before he lost his soul the second time, and I don’t think was even mentioned until he got his own show.
Rather, these are subconscious elements of Spike’s psyche. Hence the turmoil he’s been in for the last few seasons: the powerful but restrained demon spirit is in conflict with the diminished remnants of his humanity. The attempted rape was a result of both the soul and the demon wanting the same thing (sex with Buffy) and the demon losing it’s restraints. When Buffy started fighting back, and he came to his senses, part of him, as stankow put it, was thoughly repugged. Over the last two seasons Spike has been more and more disturbed by his own actions, even as his declarations of his own evilness has grown louder and louder. Yes, his baser instincts almost always win out: he tried to rape Buffy, he tried to kill that woman in the alley when he thought the chip was broken, he fed off the woman at the Bronze Dru killed for him. But each time he has struggled with his actions, either before or after. Look at the amount of time Spike spends psyching himself up before he tries to kill the woman in the alley, and contrast it with the casual way Angelus snapped Jenny Calender’s neck. Even though Spike consistently loses the struggle, the fact that he is struggling at all is remarkable, and, to me, makes him the most interesting character on the show.