Santa Claus's reindeer form an imaginary team of flying reindeer traditionally held to pull the sleigh of Santa Claus and help him deliver Christmas gifts. The commonly cited names of the reindeer are Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Donner, and Blitzen.
They are based on those used in the 1823 poem "A Visit from St. Nicholas" (commonly called "The Night Before Christmas"), which is arguably the basis of reindeer's popularity.
"A Visit From St. Nicholas", handwritten manuscript by Clement C. Moore
The 1823 poem by Clement C. Moore "A Visit from St. Nicholas" (also known as "The Night Before Christmas" or "'Twas the Night Before Christmas") is largely credited for the contemporary Christmas lore that includes the eight flying reindeer and their names.
The relevant segment of the poem reads:
When, what to my wondering eyes should appear,
but a miniature sleigh, and eight tiny rein-deer,
with a little old driver, so lively and quick,
I knew in a moment it must be St. Nick.
More rapid than eagles his coursers they came,
And he whistled, and shouted, and call'd them by name:
"Now, Dasher! Now, Dancer! Now, Prancer, and Vixen!
"On, Comet! On, Cupid! On, Dunder and Blixem!
"To the top of the porch! to the top of the wall!
"Now dash away! dash away! dash away all!"
As dry leaves that before the wild hurricane fly,
When they meet with an obstacle, mount to the sky;
So up to the house-top the coursers they flew,