Actually, Ol' Saint Nick has a number of ancestral death records. Using the Best Genealogy Tools for 2010 that I highlighted a few days ago, here's what turns up with a search on the name, Santa Claus.
FamilySearch uncovers two records in the Social Security Death Index, complete with Santa's SSN:
Birth Date: 10 Jun 1930
Death Date: 10 Sep 2008
Social Security Number: 428-48-5735
State or Territory Where Number Was Issued: Mississippi
Birth Date: 15 Jan 1944
Death Date: 26 Aug 2003
Social Security Number: 326-34-2714
State or Territory Where Number Was Issued: Illinois
Stephen Morse's wonderful site uncovers an Italian immigrant to the US in the Castle Garden database, one Santo Clausi, who arrived in New York on October 1, 1902.
Morse also has a search interface to Ancestry.com, where we find 20 Santa's, including Santa M. Claus, Santa Elf Claus, and even Santa Hohoho Claus (with an odd attached note of Other Possible Names: Kris Hohoho Kringle).
And alas, at FindAGrave we have photographic proof of the final resting place of Santa "Nick" Claus.
Santa's demise notwithstanding, I suspect folks will have a very Merry Christmas and assorted other solstice-inspired celebrations this holiday season.
Here's hoping for a prosperous, peaceful new year for all.
Santa Claus, his wife Mabel, and the six kids, from the 1930 Census. No Rudolph, though!
Visit the main page of Free Genealogy Tools for more, umm, free genealogical tools.
And don't forget to also check for your family history at Ancestry.com and NewspaperArchive.com. These are subscription databases, but they are among the most powerful research tools available for looking into family roots.