"New Year's Day" by U2
I can't help thinking there's a parallel universe where U2 broke up in 1983 and the band is best known today for the airplay this song receives every January 1st:
"Drive Somewhere" by the Vulgar Boatmen
After moving to Chicago in 1990, I'd swear I heard this song every day on WXRT, hence my assumption that it came out that year. But the song (and album) was actually released in 1989, so it makes the cut for this blog!