After reaching a certain age vampires will start to deform, to look more like animals. Joss Whedon (Show creator) says they take on
the form of their demon spirit. The Master looked like a bat,
Kakistos looked like a goat or something similar. They were both old. Giles said The
Master is as old as any vampire on record, and Kakistos's name is in ancient Greek,
meaning he would probably be over 2000 years. Therefore we know The Master is either as
old as Kakistos, or older.
Some of the things which could possibly disprove this:
Some books state, The Master as a much younger age. Well, these are just books, so I don't count it, the author was allowed some creativity, and unfortunately it contradicts the truth. Simple as that.
In the episode School Hard a vampire claims to have been at the crucifixion of Christ, which happened around 2000 years ago. The vampire showed no signs of deformation, and so it would be impossible to make such a claim. This would be like a 35 year old man saying he was in World War One. However, the way I see it, a lot of vamps don't live to deforming age, so a lot of them don't know that vampires deform with age. It's not like they go to school.
The biggest problem I hear about is that when Angel was in another dimension for hundreds of years. He never deformed. Well, there are a number of reasons why this might not have happened. If you remember, it's the demon soul that deforms the body. Angel's demon soul wasn't in control, or at least not fully. Another reason is he was being tortured. I doubt he was getting fed a whole lot. If he's not healthy, I don't think he'd grow, or change.
As vampires get older they become stronger. Some are naturally stronger of course, but the longer they live, the stronger they become. For example. The average vampire Buffy slays in the graveyard or the park can be stabbed almost anywhere on the chest and they will be dusted. An older vampire like Angel can be stabbed very close to the heart and not die. Kakistos was a very old vampire, when he was stabbed he wasn't killed, it took a large piece of wood to rip through his body to kill him. If you remember, the same thing happened to The Master. Even though his death was somewhat different then any other vampire's death ever seen on the show, this may or may not have anything to do with age. Darla was stabbed in the stomach, and didn't die either.
Since this report was first written, Angel has confirmed the theory that the deformation has to do with age. Yay!