Etymology of Yankee? A much vexed question that one, as I'm sure you know! Here's part of the Random House take on it:

"Most scholars now believe that Yankee comes from Dutch although there is disagreement about which Dutch word is the source.

Random House Webster's College Dictionary suggests that Yankee comes from Jan Kees (or Jan Kaas), 'John Cheese', a nickname for the Dutch. The -s at the end sounded like a plural to English speakers and was dropped. Proponents of this theory believe that the name was first applied to Dutch pirates by the English and later used by the New York Dutch for their Connecticut neighbors. H.L. Mencken favored this explanation, noting that the New Englanders' "commercial enterprise outran their scruples."

The other popular theory, favored by the OED, is that Yankee comes from Dutch Janke (or possibly Jantje), 'Little John', the diminutive of Jan, which was used as a derisive nickname by either the English or the Dutch in the New England states."