The common names given for Santa's reindeer in modern culture are Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Donner/Donder, Blitzen, and Rudolph. Eight of these names are taken more or less directly from Clement C. Moore's "A Visit From St. Nicholas," and the ninth from the song "Rudolph the Red-Nosed Reindeer" and the TV special based upon it.
Two of the reindeer names, Donner / Donder and Blitzen, are often the source of confusion, misspelling, and misinformation. The short facts are these: Donner/Donder and Blitzen were named "Dunder" and "Blixem" (the Dutch words for "thunder" and "lightning") in the original printing of "A Visit From St. Nicholas." In reprints of the poem, the names became "Donder" and "Blixen," then "Donder" and "Blitzen" (the latter being German for "lightning"). By the time Johnny Marks wrote "Rudolph," it was "Donner" and "Blitzen" (possibly because "Donder" was musically awkward). See Snopes.com for a thorough discussion.
In modern times, other reindeer have been named in books, movies, and television shows (such as Fireball, Leroy, Pablo, and Olive), but none have become permanent fixtures of the team.