I like to sing “One Million Bottles of Beer on the Wall”, but I’m rarely allowed to finish.
Oh yeah, Bob Rivers’ “12 Days” parody, which some people apparently attribute to Weird Al.
Whoo, I hear ya. There are some good responses here, but so many simply ignored the conditions I set up (kinda, you know, why I started the thread in the first place) that if it’s a song I haven’t heard of, I have no way of knowing whether it actually applies or not…
**Headhunter ** by Front 242.
One - You lock the target
Two - You bait the line
Three- You slowly spread the net
And four - You catch the man
Another seasonal qualifier:
You know Dasher and Dancer and Prancer and Vixen,
Comet and Cupid and Donner and Blitzen…
All eight of the ones you know, plus Rudolph for the most famous of all.
Children, Go Where I Send Thee features an alternate take on the 12 Days theme.
I came in to post that–should’ve figured one of our eclectic crowd would beat me to it!
How about The Vatican Rag :
First you get down on your knees,
Fiddle with your rosaries,
Bow your head with great respect, and
Genuflect, genuflect, genuflect!
The Men in My Little Girl’s Life by Mike Douglas
(OK, it’s probably not a complete list, but apparently he thinks it is, so it should count. ) 
Here’s a video clip of the Three Stooges singing Swingin’ The Alphabet. Do the lyrics go on to cover the whole alphabet, or just the ones in the short clip?
Why? The OP asks for complete lists, not titles with numbers in them. That song does not enumerate 99 balloons. Ditto for “Sixteen Tons,” “96 Tears,” etc.
I thought the OP was pretty clear.
The Doors - The Soft Parade
“There’s only 4 ways to get unraveled. Once is to sleep and the other is travel. One is a bandit up in the hills. One is to love your neighbor till his wife gets home.”
“Seven Nights to Rock”, by various artists:
‘Seven Days’ by Sting.
[simpsons]
Infinity bottles of beer on the wall, infinity bottles of beer
take one down, pass it around, infinity bottles of beer on the wall…
[/simpsons]
XYZ by the Tiger Lillies
Read the OP. Specifically, the last line.
Back to the OP
Thirteen Question Method by Chuck Berry. Asks all thirteen questions. I like Ry Cooder’s version best
Book Of Love by the Monotones. Lists the chapters in order.