For these purposes, “human beat box” sounds are equivalent to humming.
So, what’s the hardest song to hum/beatbox to someone and have them know it, but yet, one would recognize it in a heartbeat on the radio?
My candidate is “Love Spreads” by Stone Roses. It’s in a “Grunge Key”, which is difficult to hum in, the notes are really close together, and furthermore, after the opening riff is repeated twice, it’s replaced by a variation that sounds quite similar.
This is ancient, but “Stardust” has to be one of the more difficult songs not only to hum, but to sing.
Giant Steps is no pushover, either.
“Smells Like Teen Spirit”
(Or the variation I prefer, “Smells Like Nirvana” 
)
How 'bout some unhummable TV themse, like the themes from “ER” or “Seinfeld.”
Forgot about TV themes. A lot of them ARE hard to hum. Especially the Decade of TV Themes, the 70’s (and early 80s), what with the preponderance of wah-wah guitars and all.
(Okay, so I can hum Shaft but that’s about it.)
“Walk This Way” – Aerosmith
??
“Flight of the Bumblebee”, though one seldom hears this on the radio.
My Sharona
The bridge of Sophisticated Lady. Try to stay on pitch without accompaniment.
Rock Me Amadeus.
The Star-Spangled Banner.
Ever atempt to hum Marquee Moon by Television?
It’s impossible.
Friday on My Mind. Some really crazy modal-type guitar parts and apparent key changes. I never fail to be impressed with that song’s structure.
This has already been mentioned, but “The Star-Spangled Banner” is often considered quite hard to sing because it has a wide range from its lowest note to its highest note. The same problem would exist with humming it. A popular song with a complicated structure is “Good Vibrations” by the Beach Boys. I dare anyone to memorize it and then hum it.
Give “Up Up and Away (in my Beautiful, my Beautiful Balloon)” a try, why don’t you?
So very true. But a snap compared to Lush Life.
Loser by Beck.
Earl Snake-Hips beat me to it. Me and a few friends tried to vocally reproduce the ER theme but always end up looking and sounding like complete morons.
(we do these sorta things on friday nights)
I don’t know about hardest, but a serious effort at “It’s The End Of The World As We Know It” by REM should pretty much leave a person light headed from lack of oxygen.