The song from the 1964 animated Christmas classic Rudolph the Red-Nosed Reindeer tells us about the eight reindeer that pull Santa's sleigh. There's Dasher and Dancer and Prancer and Vixen, Comet and Cupid and Donner and Blitzen. The song also introduces us to Rudolph, the most famous Reindeer of all. What the song doesn't explain is why there are only seven reindeer hitched to Santa's sleigh when Rudolph saves Christmas. According to IMDB, there was a subplot about the missing reindeer that was dropped from the film. Which pair of reindeer did Rudolph replace when he saved Christmas in the 1964 animated classic?
Scratcher: Don't mention that name.
Scratcher: I was all set to be one of santa's reindeer when he came along.
Winterbolt: Santa fired you to make room for Rudolph?
As for the other reindeer, as explained in the other answer, he never existed.
Well I can't say I have confirmed this, but this Wikia on Christmas specials claims to have:
There are only six reindeer in addition to Rudolph, instead of the usual eight. It has been confirmed that there are only six reindeer because of the time that the creators had to make them, and because they were rather expensive to build.