In the Buffy universe there are vampires that are bald, pointy-eared and bat-nosed. Vampires like Angel and Spike have been around for over a century and not aged but there are some that show the passage of time on their face so I must ask: do vampire ages after a certain number of centuries or is there a separate bread that can age?
The Angel episode "Darla" seems to imply his appearance is a function of his great age. From the transcript here:
Angelus: "It's not stuck like that now is it?"
The Master leans in on him with a growl.
Darla: "The Master has grown past the curse of human features."
Angelus: "I'm not gonna get a bat-nose like that, huh? Am I?"
Master: "Very few vampires are cunning enough to have lived as long as I have - which you've now (The Master grabs Angelus by the front of his coat and throws him across the room) demonstrated."
And as noted in the entry on the Master from the Buffy wiki, his monstrous appearance was also somewhat similar to the Turok-Han Vampires, the "Ubervamps" of Buffy season 7 who were even older than the Master (in the Buffy episode 'Never Leave Me', Giles says 'As Neanderthals are to human beings, the Turok-Han are to vampires.') And as Izkata mentioned in a comment, we've also seen the example of Kakistos, a very old vampire seen in "Faith, Hope, & Trick", of whom Giles said "'Kakistos' is Greek. It means the worst of the worst. It's also the name of a vampire so old that his hands and feet are cloven."
cde also pointed out in a comment that we know a vampire is a sort of combination of a human and a demon sharing the same body (the human soul is normally gone, but the human memories and mental abilities and many personality traits seem to remain)--in the Angel episode "Through the Looking Glass", Angel & co. travelled to a magical parallel world called Pylea, where Angel showed more human characteristics (ability to withstand sunlight, a reflection) when in human form, but when Angel tries to change into his vampire form to fight, he instead turns into the demonic-looking Van-Tal (the name used by the locals of Pylea in the subsequent episode "There's No Place Like Plrtz Glrb"). And soon after he changed there was this dialogue:
Wesley: "Only his human side as surfaced since we've been here..."
Gunn: "You mean being able to walk around in the sun - seeing his reflection, like that?"
Wesley: "Yes. And now, for whatever reason he's accessed his demon, but he can't find the balance he normally would in our world. His demon-self has totally overcome his human side."
Gunn: "So that's what the thing inside of him really looks like?"
Wesley: "In its purest form."
So as cde said, it seems reasonable to speculate that in older vampires the demon side has become more dominant over the human side, and that also manifests physically.
On Buffy's universe, even "handsome" vampires like Angel or Spike adquire "beast" facial traits under rage, or combat situations.
It's not said on the show, but it can be implied that the human appaerance is something they have to maintain on purpose (it's obviously a lot easier to feed and live between humans if you're not a horrid monster).
Usually, vampires without this human aspect, are always very old or isolated, which implies that they had trascended the need to live among humans.