In addition to songs like "Ball Game," where only the chorus is remembered, there are a lot of American "standards" (especially those originally written for the musical theater) that originally included an introductory passage or "verse," sung once, that preceded the well known repetitive structure of verse/chorus/bridge. These intros are routinely omitted and forgotten.

I wish I could give a good example, but can't. I'm sure that many familar tunes by Gershwin, Irving Berlin, Cole Porter, etc., would fit the bill.