I live in Chicago, so I’m the authority on how it’s pronounced. 
Count me in with the folks who have a hard time with H - L. I don’t have to sing it, nececarily, but I do have to start at H and recite my way to the letter I’m looking for.
It’s funny that so many people have problems with this one section…
Mmm.
Today I was looking for an “H” file and couldn’t find it. I had filed it behind the "I"s. Next time I shall sing.
I spent so many years as a secretary and file clerk that I stopped having to sing the alphabet song as I filed.
I learned to hum it to myself instead.
Let’s not even start talking about multiplication tables, okay?
A few years ago, a friend of mine was pulled over in the U.S. late at night on suspicion of driving under the influence. (He wasn’t - he was just tired.) As part of the field sobriety test, the cop asked him to say the alphabet. He started out OK, but by the time he got to “e” he had started to sing. Much embarrassed, he got a hold of himself, only to drift back into the infamous “alphabet song” a few letters later. The cop, meanwhile, was fighting a valiant, though losing, battle to maintain his professional demeanor. According to my friend, the officer was trying so hard not to laugh at the spectacle of my friend trying not to sing the alphabet that he looked as if he were having some sort of seizure.
By the time he had struggled through to “z,” it was all the cop could do to waive off my friend and stagger back to his patrol car.
Well, you know those Founding Fathers had a lot to do with whether a month as 31 days. It’s in Amendment 522. 
WashAdJeMadMonAdJackVanHarrTyPoTay
FillPierceBuLincJohnGrantHayes
GarArtCleveHarrCleveMacRoo
TaftWilHardCoolHoovRooTru
IkeKenJohnNixFordCarRea
BushClintBush
Not a song, but a memory aide.
DooDooDooDooDoo DooDooDooDooDooDoo DooDooDooDoo SEVEN!
Gotta love it.
I don’t have to sing the alphabet, but this reminds me of a story. A friend of mine from India who I guess had learned English not as a young child had a more elaborate song, that went something like “A for apple, B for boy…” Out of curiosity I asked him what X was for, and he gleefully replied, “Xmas tree!”
As soon as I see/hear “A is for apple” I immediately go straight to J:
I don’t know about you, but you could get into a heap of trouble with that last line if anyone only half-hears you.
Another singer here… tho I can start somewhere in the middle (Q R S, T U V) if I am alphabetizing something near the end.
If I’m counting by fives, I use the rhythm from the Schoolhouse Rock video …
Somewhere I have an Animaniacs CD where Wakko recites the states & capitals of the USAto the tune of “Turkey in the Straw” and Yakko does the nations of the world to the tune of the “Mexican Hat Dance”.
Vietnamese has an alphabet and is also a tonal language. Does reciting the alphabet with the tones constitute singing it?
How many people have memorized Tom Lehrer’s “Elements” song? (It’s the periodic table sung to “Modern Major General.” Pretty cool.)