etymology - Why does Polly want a cracker?

While there are a number of sources that attribute the origin of this phrase to R.L. Stevenson's Treasure Island (pub. 1883), or alternatively, to the National Biscuit Company (Nabisco, c. 1876) which used it as a popular slogan, neither of them appears to be the right one. As James McLeod has pointed out in another answer, "Polly want a cracker" can be verified to have been in use even before these dates.

The earliest entry in Google Books is from Bunkum Flag-Staf and Independent Echo", a satirical fake newspaper published in The Knickerbocker (or, New-York Monthly) magazine, Volume 34, in 1849. The reference to Polly's crackers can be seen in the following excerpt:

A radio show named A Way with Words has also attempted to trace the roots of this phrase. According to the host, the earliest reference he could find was the following cartoon from 1848 in another satirical magazine named The John-Donkey:

The use of cracker in the cartoon is a pun on the word for the biscuit as well as the fact that the boy is ready to crack the skull of the parrot open, presumably for annoying him (perhaps by asking him for a cracker?). The hosts of the show go on further to make a connection between the use of crackers on ships (as long-lasting food) and perhaps parrots being on board as well. At any rate, they conclude that even in 1848, parrots named Polly wanted crackers and that the phrase might have been commonly used.

Now, cracker biscuits were invented in 1801 (or perhaps earlier in 1792) which should date this phrase. Incidentally, the use of the name Polly for a parrot can apparently be dated to at least 1606 to Ben Jonson's play, Volpone. According to the source, the OED (somebody please clarify) expounds on this matter thusly:

Polly is a diminutive of Poll "as a female name, and name for a parrot," and Poll, altered from Moll, familiar form of Mary, is the traditional name for any parrot. The earliest quotation the OED gives for Polly as a name or designation for a parrot is from Ben Jonson's "Epigrams," 1616.

In conclusion, there is no concrete proof of the exact origin of the phrase. However, my best guess is that crackers became the staple food/snack for pet parrots who ended up parroting their owners during feeding time - "Polly, want a cracker?". I believe that the phrase was popularised by Nabisco's slogan and has been in use ever since. In other words, this exercise was quite pointless; but, I wouldn't have it any other way :)