The answer is Yes, No, and Maybe!
If you were born a Taylor you may have grown up with a family story about being related to Zachary Taylor. Well, in one sense you are.
Just as you are related to Confucius, the Chinese Philosopher, or Cleopatra, the daughter of Ptolemy XII and ruler of Egypt. In that sense, as a member of the human race, you are cousins with Zachary Taylor, as well as cousins with Confucius and Cleopatra.
If you mean that you are a direct descendant of Zachary Taylor (November 24, 1784 – July 9, 1850) the American military leader and the twelfth President of the United States, it is likely that you are not. The reason is that Zachary had only one son, Richard "Dick" Taylor (January 27, 1826–April 12, 1879), Confederate States Army General. Richard Taylor had two sons, Richard (born in 1857) and Zachary (born in 1860), who both died during the war after contracting scarlet fever.
Thus, there are no direct male descendents of Zachary Taylor, unless 150 years of public interest and genealogy has failed to locate another male heir.
If your claim to being related to Zachary Taylor, the 12th President of the United States, is based upon having the Taylor surname, you could still be related to him as a collateral relative. That is, your line could trace through his brothers, uncles, great-uncles, great-great uncles, and so forth. To check this go to the extensive list of his Taylor line, found at http://wc.rootsweb.ancestry.com/cgi-bin/igm.cgi?op=GET&db=zachary-taylor&id=I1. Or see http://homepages.rootsweb.ancestry.com/~pmcbride/james/f061.htm.
But wait, there are still two other options. One is that you are a descendant of Zachary Taylor through the line of one of his daughters. Which you can investigate through the links provided. The other option is to be a biological relative of a heretofore unidentified line. That option would require DNA work to prove…
For more research:
Lalia Wilson, granddaughter of James Bentley Taylor, writing for the Taylor DNA Project