This one is always coming up; it was used for practically everything during the 19th century. Star of the County Down seems to have been written in the early 20th century, but has been so widely recorded commercially that almost everybody calls the tune by that name nowadays. Its earliest recognisable appearance in print was with the song Gilderoy (early 18th century, but broadside examples without music date from the latter 17th) in England, but the tune -in that form- may be Scottish or English. Simpson (The British Broadside Ballad and Its Music, 1966) considers it likely that the whole "tune cluster" (Dives and Lazarus, Come All You Faithful Christians, etc.) derives ultimately from an English tune of the mid 17th century, The Clean Country Way.

All this has been said here before, of course. Look especially for Bruce Olson's comments on the subject.