I'll submit the 1970s song "Run Joey Run" as a so-bad-its-fun song. It's the one about a guy who wants to do right by his pregnant girlfriend, but her mean old dad is gunning for him. Dad accidentally shoots the girlfriend, who goes to heaven with a chorus of fake-portentous "aaawww-aaaahhhs."

I find truly over-the-top songs such as this more enjoyable than mediocre songs such as "My Heart Will Go On."