The history of "Santa Claus" is a convoluted one. His roots are many and varied, with each country and culture seeming to contribute something to the legend. Here are the main ones:
His name comes from the Dutch "Sinterklaas", a.k.a. St. Nicholas of Myra (patron saint of, amongst other things, prostitutes!). As a christian saint, he was acceptable to the American people who would shape and popularise the modern image of Santa Claus. But what most Americans did not realise was that the bulk of his legend came from much older pagan beliefs.
The oldest known Santa analogue is the Norse god Odin, or Woden (from whom we get "Woden's day", i.e. Wednesday). During Yule, he would hold a great hunting party. Children would leave out their boots filled with straw, sugar or carrots, to be consumed by his great eight-legged horse Sleipnir. (Some see a connection between the eight legs and the eight reindeer of Santa). Odin would then thank the children by leaving sweets and gifts in place of their offerings. Odin was usually portrayed as an old man with one eye and a long beard — not exactly the Santa we know today!
A character who would be more familiar to us today is the Russian Ded Moroz (meaning "Grandfather Frost"), a red-coated, white-bearded gift bearer. Instead of coming in the night, though, he would arrive to present his presents to children in person, on New Year's day. The original Russian gift-bearer was St. Nicholas, who began to be replaced by Ded Moroz in the 1800s — a secularisation of St. Nick that predates the same transformation in the west by over a century!
Yet another proto-Santa candidate is the Scandinavian Tomte. A small brownie-like creature with a white beard and red pointed cap, it was a regular fixture on christmas cards thanks to one Jenny Nyström, children's author and illustrator. It became assimilated into the figure of St. Nicholas, which led to earlier Santas often being pictured as small and elfin. Those versions seem to have disappeared now in favour of full-size Santas — only the pointy hat remains as a nod to this creature.
A completely seperate gift-giver was invented by Martin Luther; the Christkind (Christ child). Popular in southern Germany, Switzerland and Austria, it is a blond creature with angel's wings, which is only ever glimpsed. There is some confusion over whether it is supposed to be Christ as a child, or a figure that delivers presents to the infant Christ. It was brought to America by immigrants as the "Christkindlein", now anglicised as "Kris Kringle".
And finally "Father Christmas" is the British winter figure. (He was originally "Old Winter", then "Old Christmas", then "Old Father Christmas".) An elderly man from each village would dress in furs and visit each house. He was thought to carry the spirit of winter in him, and so at each house he would be plied with food and drink, in order that winter would look kindly upon that household. (Not a bad job, eh?) His name was later applied to the more modern Santa figure.
And there you go. I had originally intended to cover the fascinating subject of Santa's companions as well, but I've gone on for quite long enough already. Perhaps tomorrow.