Only if the NBC trichord counts.
It’s a shame… TMBG’s “Why Did You Grow a Beard?” clocks in at 1:05.
Not really a whole song itself, but I always liked the ‘Whiskey & Wine foreplay’ track on Lisa Brokop’s ‘undeniable’ album. (W&W was one of the singles, and the foreplay is essentially an accoustic rehearsal of the chorus, with some impromptu comments about it.)
And, of course, “Bad Horse Letter” from the Doctor Horrible soundtrack!
If we’re including TV themes, *Twilight Zone *is only 0:29.
Bad Religion - Out of Hand from the compilation Short Music for Short People, an excellent album of short punk songs from Fat Wreck records.
Drunk Drivin’ by Sublime is a nice little ditty that clocks in under 19 seconds.
The Dead Milkmen have a couple: “Junkie” and “Takin Retards to the Zoo” (no, not very PC at all)
If WMP is reading things right, a lot of funny Monty Python songs are under 1 minute…“the Penis Song”, “Sit on my Face”, “Henry Kissinger”, “Spam Song”, “I’ve Got Two Legs”, etc.
The Violent Femmes also have a couple short ones - “Old Mother Reagan” and “Dahmer is Dead”.
The Beastie Boys “Tough Guy” actually feels too long at 58 seconds.
“Sunshine and Clouds (And Everything Nice)” from Clap Your Hands Say Yeah is unfortunately two seconds over a minute.
Many of the songs from the TV series “Home Movies” only play for less than a minute but fade out as if there’s more. Although “Turn Into a Bug” from the Kafka musical is complete at less than 30 seconds.
Only if “Haaaaaaaaaawt Pocket” and “Caliente Pocket” count…
It could be said that “Crowned Miss Fire Prevention” is the ultimate Heavy Blinkers song, and it’s about 30 seconds long.
They also did Pool Shark, which is 57 seconds long and another favorite.
Bring the Boys Back Home by Pink Floyd always has me singing along in that crazy Roger Waters voice.
Boa Constrictor by the Magnetic Fields is also a good song.
I have to agree with the OP though, nothing beats Her Majesty in the sub 1:00 category
edit: I have to add The Power to Believe 1: A Capella to the list–it was the first song on the first King Crimson album I heard (yea I got into them late) and it really pulled me in.
I Like Food by the Descendents is possibly my favorite super short song ever - I think it’s 17 seconds. It’s even inspired a cookbook.
It almost takes longer to say thetitle of Hearts Frozen Solid, Thawed Once More by the Spring of Rage, Despair, and Hopeless by AFI than it does to listen to it.
Dylan’s Talkin’ Hava Negilah blues at 0:52.
And of course there’s “ALL” and “No! ALL”.
Nazi Punks Fuck Off by the Dead Kennedys is 1:03.
Dead Kennedys, Short songs
its about 19 seconds of punk with the opening line (before the song starts) being “Rick Wakeman eat your heart out”
Two more short ones by the Beatles: Maggie Mae and Dig It. Maggie Mae is pretty good.
Hands down (for me): The original **Mission: Impossible** theme song.
I just came in to mention this album. 
Concur.
Technically, John Denver’s The Music Is You is only about 30 seconds long. But he repeats the verse and yodels, so the recorded version is actually about 90 seconds long. If you listen to his Evening With John Denver album, you’ll hear it in its proper length.