The Cockroach That Ate Cincinnati - Rose and the Arrangement
It’s the form of an early version of the song. The song as recorded is ABABCAB followed by an extended outro.
“Regretting what I said to you when you called me at 11:00 on Friday morning to tell me that 1:00 Friday afternoon you were gonna leave your office, go downstairs, hail a cab, to go out to the airport, to catch a plane, to go skiing in the Alps for two weeks. Not that I wanted to go with you; I wasn’t able to leave town, I’m not a very good skier, I couldn’t expect you to pay my way, but after going out with you for three years, I don’t like surprises.” - Christine Lavin
“Dinner Music for a Pack of Hungry Cannibals” - Raymond Scott
My understanding is that that was, in fact, true at one point in the song’s development, but they changed the order of the segments in the final version.
Edit: I posted before I saw pulykamell’s better description. 
For accuracy: “Title of the Song” - DaVinci’s Notebook.
For silly length: “Jeremiah Peabody’s Polyunsaturated Quick-Dissolving Fast-Acting Pleasant-Tasting Green And Purple Pills” - Ray Stevens
For reals though: “Life By The Drop”, Stevie Ray Vaughan.
Mozart’s Canon in B flat major, K. 231, “Leck mich im Arsch (Lick Me in the Ass)”.
I’ve never been a really big Jethro Tull fan, but Skating Away (On the Thin Ice of a New Day) is one of my favorite song titles ever.
Also, Pink Floyd’s Piper at the Gates of Dawn is one of the greatest album titles of all time.
Some paired names from Robert Wyatt’s Rock Bottom:
“Little Red Riding Hood Hit the Road”
“Little Red Robin Hood Hit the Road”
“Alifib”
“Alife” The last letter is the key they’re in.
Also, the titles on Soft Machine’s Volume 2
“Pataphysical Introduction – Pt. 1”
“A Concise British Alphabet – Pt. 1”
“Hibou, Anemone and Bear”
“A Concise British Alphabet – Pt. 2”
“Hulloder”
“Dada Was Here”
“Thank You Pierrot Lunaire”
“Have You Ever Bean Green?”
“Pataphysical Introduction – Pt. 2”
“Out of Tunes”
“As Long as He Lies Perfectly Still”
“Dedicated to You But You Weren’t Listening”
“Esther’s Nose Job” (A Thomas Pynchon reference).
“Fire Engine Passing with Bells Clanging”
“Pig”
“Orange Skin Food”
“A Door Opens and Closes”
“10.30 Returns to the Bedroom”
She Got The Gold Mine (I Got The Shaft), Jerry Reed
Poisoning Pigeons in the Park - Tom Lehrer
The Masochism Tango - Tom Lehrer
My Guitar Wants to Kill Your Mama - Frank Zappa
A slight detour into a comedy album, but it certainly fits the “song titles that have nothing to do with the content” nature of this thread. David Cross has always titled his standup material with tracks like…
(this is 2004’s It’s Not Funny)
Side One:
Certain Leaders in Government Look or Act like Certain Pop Culture References! – 4:51
Women, Please Rinse Off Your Vagina and Anus! – 5:10
I’ve Taken a Popular Contemporary Pop Song and Changed the Lyrics to Comment on the Proliferation of Starbucks in My Neighborhood! – 3:16
A Rapid Series of Comical Noises! – 3:57
Although Indigent, Rural Families Have Little to Say in the Matter, Third Rate Public Education Has Kept Them Ignorant and Thus, Great Sources of Ridicule! – 2:48
My Child is Enthralling, Especially When It Says Something Unexpectedly Precocious Even Though It Doesn’t Understand What It Just Said! – 8:38
Side Two:
My Immigrant Mom Talks Funny! – 13:37
When It Comes to Jews, Behavior One Might Perceive as Obnoxious and Annoying I Present as ‘Quirky’ but It’s Okay to Joke About It Because I, Myself, Am Jewish! – 6:01
Pandering to the Locals! – 7:13
Even Though I Am in the Closet, That Won’t Prevent Me from Getting Cheap Laughs at the Expense of Homosexuals! – 2:37
Weathermen Have Become, for the Most Part, Obsolete! – 2:53
When All is Said and Done, I am Lonely and Miserable and Barely Able to Mask My Contempt for the Audience as I Trot Out the Same Sorry Act I’ve Been Doing Since the Mid-Eighties! – 12:51
I’ll take Thank You (Falettinme Be Mice Elf Agin) by Sly and the Family Stone.
Incidentally, Magazine covered it with a slightly amended title:
(Iwanna) Thank You (Falettinme Be Mice Elf Agin).
Nice touch.
That aside, there’s many a Hank Wangford song with a great title:
Cowboys Stay On Longer
Never Wear Mascara If You Love A Married Man
Joggin’ With Jesus…
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John Wayne is Big Leggy - Haysi Fantayzee for the sheer obscurity
In-A-Gadda-Da-Vida - Iron Butterfly for the back story (A drunk band member trying to say “In The Garden of Eden”)
Wang Dang Sweet Poontang - Ted Nugent for the cheesiness.
Well, if we’re going to go down the “titles that have nothing to do with the song” road, we need to include Cream’s “Badge.” As I understand it, a handwritten “bridge” on the score was misread as “Badge.”
Personally, I have always been charmed by Jack Bruce’s (co-writer) “Theme for an Imaginary Western.”
Meatloaf had some good titles on some very angry songs: “Everything Louder Than Everything Else”, “Life Is A Lemon And I Want My Money Back”.
Elton John did the slightly ironic “This Song Has No Title”.
Los Campesinos!, “The Sea Is A Good Place To Think About The Future”.
Simon & Garfunkel’s “A Simple Desultory Philippic”
I hope this wasn’t already mentioned above!
How can I miss you if you won't go away. Eldon HuntAll I could think of, and I wanted to be in on this thread!
(snip)
In a similar vein, on Kyle Kinane’s album Whiskey Icarus (which I highly recommend, by the way), all the track titles are taken directly from the album Destroyer by KISS. It starts with “Detroit Rock City”, through “Flaming Youth” and “Beth”, and ends with “Rock and Roll Party”. The track titles have nothing to do with the content, of course.
He did the same thing with Death of the Party (track titles are from Cheap Trick’s Dream Police) and I Liked His Old Stuff Better (track titles are from NWA’s Straight Outta Compton, changed slightly to “This Track Is Not Called whatever”)
You left off the best part: “(Or, How I Was Robert McNamara’d Into Submission).”