Does Santa have 8 or 9 reindeer? What are their names?

There are eight reindeer. If you count Rudolph, then there are nine. The eight reindeer are: Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Donner and Blitzen (which means thunder and lightning in German). Note: some say Donder instead of Donner.

There were 8 original reindeer in "Twas the night before Christmas":

Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Donner and Blitzen!

Rudolph only exists because of the song. He was a late addition.

So, the answer is 8 if you're talking about the poem/early history. The answer is 9 if you're talking about how we'd count them today.

EIGHT.
The original poem ''Twas the night before Christmas' or
(or A Visit from St. Nicholas) by Clement Clarke Moore.

Contains the verse:

With a little old driver, so lively and quick,
I knew in a moment it must be St. Nick.
More rapid than eagles, his courses they came,
and he whistled and shouted and called them by name:

'Now Dasher! Now Dancer!
Now, Prancer and Vixen!
On, Comet! On, Cupid!
On, Donner and Blitzen!
To the top of the porch!
To the top of the wall!
Now dash away! Dash away!
Dash away all!'

The 'ninth' ?
Although he's a good friend of Santa's, Rudolph was not one of the original reindeer. He came later with the popular Christmas song, 'Rudolph the Red Nose Reindeer.'

Rudolph didn't exist until 1949 !!!!

http://www.celebratelove.com/rudolph.htm

Eight reindeer in the original poem, including Donder (a Dutch name) not Donner (a German name). Rudolph was not one of the original eight, because all of the other reindeer used to laugh and call him names. Then one foggy Christmas Eve... and the rest is history. Or rather, mythology. Rudolph went on to lead the reindeer and become the ninth.

Two of Santa's reindeer were originally named "Dunder" and "Blixem," not "Donner' and 'Blitzen."
http://www.snopes.com/holidays/christmas/donner.asp