If a song is good enough (don't ask me to define what might make a song "good"!), it can lack rhyme without the listener even noticing that anything is amiss. I think that is true of "WMT" and a few other classics mentioned above.

One outstanding and well-known lyric that has no rhymes at all is Woody Guthrie's "Deportee." I knew this song for years, and sang it regularly for a while, without taking conscious note of its lack of rhymes. It's only upon re-learning it within the last year that I noticed. Maybe that's because I learned it the first time strictly by listening and repeating, whereas the second time around I printed the lyrics from the internet and read them off a page.

Another thing I learned about "Deportee" only recently is that Woody never put it to music, or at least that he didn't write the currently-known melody. I think it's even more remarkable that such a "folk poem" NOT set to music would feature a very regular meter, readily adaptable to song form, but no rhymes.