The original "Gentle Annie" is, as a couple of prior posters have said, most definitely a Steven Foster song from the 19th Century. I agree, that it seems to have inspired some "knock-offs" that have taken on a life of their own. For provenance, I suggest anyone interested go to the Steven Foster Archive at, I believe, the Johns Hopkins University website. There, you will find a first edition print of the sheet music. The story goes that it was written by Foster as an Ode to a young girl, daughter of friends of his, who died after after being run over by a derry. If that's true, I can't imagine Foster's very bittersweet lyrics were much consolation to the parents.

On the issue of "knock-offs", and while I do not know this, I'd bet $100 that McCartney's, "Here, There and Everywhere" came to him after hearing the Foster tune. The verse chord progression is identical. The very large interval in the verse is also right out of Foster's piece. Taking it one step further, "Longer Than", by Dan Fogelberg is also, essentially, the same song, musically.