Robert Burns (1759 - 1796) set to a folk song. It is a song of nostalgia for the old days, and on New Year's Eve the "old days" are the days of the previous year.
You can hear it sung by the U.S. Army Chorus via Naxos Music Library by clicking this link. (Ball State login required)
The Music Collection includes song books that are old enough to be out of copyright (i.e., published before 1923). One song book includes an arrangement of this classic song - with all the original stanzas - for you to review before celebrating New Year's Eve (click to enlarge):