I thought of a few examples, but want some more. Don’t count songs with nonsense lyrics or instrumentals without lyrics. Don’t count bilingual songs (unless neither of them is English, or if the English portions are commonly omitted). Don’t count songs primarily popular among immigrant populations or others fluent in that language.
Basically, songs an American monoglot could sing along with, but couldn’t translate.
Ue o Muite Arukou - Kyu Sakamoto
whistles a melancholic tune