I guess I would consider a song traditional if the author is unknown, or maybe if it's old enough for the "copyright" to have expired a couple of hndred years ago, like "The House Carpenter" mentioned above.

It's often true for me that a song like "Barrett's Privateers" has something about it that doesn't sound quite right for a truly traditional song, though I can't exactly put my finger on it. Too smooth, or something. On the other hand, Archie Fisher's "Witch of the Westmorland" is about as perfect a fake as ever I heard--no niggling "what's wrong with this picture" feeling about that one.

John Connolly's "Fiddler's Green" is a fine example of another perfect "traditional" style song, as was mentioned above. Chanteyranger, Bill R and I were vastly amused to hear it played on a squeezebox in a pub scene in a movie set during the American Civil War. The same movie used Gordon Bok's "Clear Away in the Morning" as a major and meaningful theme in the story, with an Irish character claiming his mother had sung it to him when he was a child. The fact that the producers apparently thought "Fiddler's Green" was traditional was highlighted by the fact that Gordon Bok was listed in the movie credits, but John Connolly was not.