Davy's "Farewell" knocked me out when I heard Fess Parker sing it on Disney's Alamo episode. But the fact is, he didn't write it.

The poem's initial connection with Crockett is its appearance in Chapter II of the one-time bestseller "Col. Crockett's Exploits and Adventures in Texas," first published in the summer of 1836, a few months after Crockett's death. Though the book was marketed as fact to a trusting public, Crockett's biographer James Atkins Shackford decisively exposed the "Exploits" as a money-grubbing hoax suggested by the Philadelphia publisher E. L. Carey and carried out by Richard Penn Smith, a successful novelist of the period. The fakery was revealed in print as early as 1839 (and again by Edgar Allan Poe in 1842), but Smith's fraud is so entertaining that apparently few people wanted to believe Davy's "Exploits" weren't the real thing.
   
Smith made the story up. We know Crockett died at the Alamo, but little is known of the details of his "adventures" in Texas, except for the significant fact that he signed an oath of allegiance to the new Texas government. That was more than a month before he reached the Alamo.

For the evidence, see Shackford's biography, "David Crockett: The Man and the Legend" (1956), esp. pp. 273-81.

As for the "Farewell," if Penn didn't write it, he stole it from someone (not Davy) who did.