That suggests a question: what is the difference between you, me, wedrifid, and others who don't see the humor ... and NancyLebovitz et al. who do?
I like xkcd and Terry Pratchett (though more for the ideas and attitude than the humor-- the humor is apt to be pretty stereotyped).
I like good single puns, but have lost a good bit of my taste for long series of puns on a subject. I blame Anthony and Robinson.
I like one-liners and paradoxical humor.
Sometimes I like slapstick. I thought the movie Noises Off (screwball comedy leaks from a play into the lives of the cast) was extremely funny. There's a consensus that a good stage production is twice as funny, which is hard for me to imagine. In any case, as ...
and get nothing!
Seriously, this strikes me and a lot of people as pretty funny, but isn't much like the typical joke.
Edited to add: Poll and discussion. Short version: being amused by the song is rarer than I would have thought, though the LW consensus may be usually strong.