The Master
THE bad guy of the first series the master is the most powerful vampire in the world. Over sixty years ago he travelled to America but not just to feed on American flesh. He was here for a more omnious reason.
The Master is the leader of the Order of Aurelius. Joss Whedon says that his real name is Heinrich Joseph Nest and is around 600 years old, even though this is never revealed on screen.
The Master was drawn to America because of the Hellmouth (a real evil magnet), he was a worshipper of the Old Ones, a race of demons who ruled the Earth before humankind. The Master wanted to open the hellmouth to release the Old Ones and join them in ruling the earth. (in a Bond bad-guy sort of way).
However, like all bad guys he was foiled, by an earthquake of all things. In 1937 an earthquake shook Sunnydale (being in Calafornia) swallowing half the town including an old church which became The Master's underground lair (and here's us thinking vampires can not go near scared ground). However, his luck was even worse than just that. The Master managed to get himself stuck, "Like a cork in a bottle". And there he stayed, but not for lack of trying though.
In the first episode he trying the use the rite of the Harvest to free himself, then he walked the earth in Billy Palmer's dreams in "Nightmares", then in the final episode of the first series he did get free, once he had lured Buffy to his lair.
After drinking Buffy's blood he was freed from the Hellmouth and the Hellmouth itself opened finally, allowing the Old Ones (a bug bunch of tentacles) to come through. Luckily, Buffy was revived by Xander and went after him which led to a showdown in the school library where he was impaled on a piece of Library furniture.
Giles, Xander and Willow buried his bones in the cemetery, and that, they thought, was the end of it. If only life was that simple. At the beginning of the second series a group of vampires, led by the Anointed One dug up his bones again and tried to resurrect him. Once again Buffy saved the day by facing her fears and smashing his bones into talc with a slegehammer.
As far as we can tell The Master is finally gone, but with a series like this he COULD be back.