hmmm - I think my pipes are just a wee bit too loud - gotta get me some parlour pipes…
I’m partial to Goodnight demon slayer
Interesting username/post combo.
No kids of my own, but I used to babysit a lot, and I sang a lot of “Lemon Tree” and “Blackbird,” too. And I never even got to live through that era! Also “The Sound of Silence,” because I know all the words, not cuz it’s at all ironic to screaming infants. 
I sing Bob Marley’s “Three Birds” and one that my mom sung to us (that was from her grandmother):
Kitty Kitty Puss
Riding in a wagon
Hop up Kitty Puss
Your tail is a-draggin’
Hop up Kitty Puss
Hop up higher
Hop up Kitty Puss
Your tail’s in the fire
Poor little Kitty Puss
Poor little feller
Poor little Kitty Puss
Died in the cellar
Hop up Kitty Puss
Hop up higher
Hop up Kitty Puss
Your tail’s in the fire
There’s about a million verses, but those are the only two I can ever remember.
“Embraceable You” and “Love is Here to Stay” for my daughter and son, respectively. They both had a lot of Gershwin, Cole Porter and Richard Rogers sung to them when they were infants.
Pearl Jam has a nice lullaby in their catalog: Around the Bend
Another nice one is Blue Shadows on the Trail, an old Sons of the Pioneers song.
MLF Lullaby by Tom Lerher
This thread title made me think of the scene from British comedy The Royle Family in which two of the characters sing the instrumental opening of “No Surprises” by Radiohead to the baby as a lullaby.
I sing “Dream a Little Dream” to my daughter as well, but the one that always gets her to settle is “Curly-Headed Baby”, a beautiful Paul Robeson classic. (I should mention that I use this version (starts about 2:09) rather than than the earlier, considerably less politically-correct (and less applicable to a pale blonde child) version.
I’ve sung this to my son since he was born, too. That’s “his” song and he doesn’t want me singing it for the new baby we’re expecting in November, so I’m thinking I’ll have to learn the words to “It’s a Wonderful World.”
I also sang him Oh, Shendandoah and Auld Lang Syne. His favorite, though (particularly when he got older) was Oh, Holy Night because I changed the words on the fly every time I sang it to him.
The first time I was called upon to sing a lullaby to my infant daughter, the only lullaby that came to mind was Lullaby of Broadway.
But it became a much-beloved routine.
I also became a dad at 40 (in 1994). My lullabyes were mostly old folk songs, with a few other things mixed in:
Jamaica Farewell (“Sad to say, I’m on my way, won’t be back for many a day…”)
They Call the Wind Maria
Four Strong Winds
If I Had a Hammer
The Riddle Song (“I Gave My Love a Cherry”)
Blowin’ In the Wind
Where Have All the Flowers Gone
Puff the Magic Dragon
The Unicorn
This Land is Your Land
Goodnight Irene
500 Miles
Mr. Tambourine Man
Michael Row the Boat Ashore
The Circle Game
You Are My Sunshine
The Baby Tree (from “Blows Against the Empire” by Jefferson Starship)
When the little Torqueling was but a few months old, one night she started crying and would not stop. I suggested we sing, but in our frazzled desperation we couldn’t think of good kiddie songs. The only song that came to mind was…“The Gambler.” Yep, Kenny Rogers. Soothed that kiddo right down. I still sing that one sometimes.
These days, I’m running out of songs. Most nights, the little Torqueling falls asleep on me, after we read a few books together. The routine goes: read the books, lay on Daddy’s chest, Daddy sings until little one is asleep, Daddy carries little one to bed.
But she’s gotten tired of all my standards. I ask her what she wants me to sing, and lately I think she just says “no” until I say a title she’s never heard before.
Some of the kid songs she’s gotten tired of:
The Fox Song
The Green Grass Grew All Around
Polly Wolly Doodle
The Echo Song
Big Rock Candy Mountain
She’ll Be Coming Around The Mountain
Hole In The Bottom Of The Sea
And some “unorthodox” ones she now nixes:
Lazybones
Ain’t Misbehavin’
The Gambler
In The Jailhouse Now
She’s An Angel
Birdhouse In Your Soul
As you can see toward the end there, I’ve started working through various They Might Be Giants songs. I’ve sung “Dr. Worm”, “Ana Ng”, “Hey Mr. DJ, I Thought You Said We Had A Deal”, and “Till My Head Falls Off” at various times. Last night I went through “Someone Keeps Moving My Chair” and “Lucky Ball & Chain” before she fell asleep. Sing 'em slowly enough and soothingly, and they work quite well.
Oh, and perhaps worst: I have sung Tom Lehrer’s “Irish Ballad” to her before as she drifted off to sleep. That either makes me Monster Dad, or Awesome Dad, I’m sure.
No lyrics, but when my daughter was just a little Kunilette, I foundthis settled her down right away and put her to sleep before it was over.
My Nephew’s favorite lullaby was Dion’s Abraham, Martin & John.
I’ve sung Phoebe’s song about cows (from Friends) to my daughter. Mind you, she’s too young to understand what I’m saying and I’ll probably have to stop doing it soon.
*Oh the cow in the meadow goes moo!
Oh the cow in the meadow goes moo!
Then the farmer hits it on the head with a hammer
And that’s how we get hamburger!
Nooooooooow…chickens!*
My sister and I had Run in Cadence with the U.S. Marines.
I was always fond of My Grandaddy was a Horse Marine.
Doesn’t this seem like something Susan (Pratchett reference: DEATH’s granddaughter) would sing to her children??
I sang The Riddle Song
Hush, Little Baby
most of Peter, Paul, and Mary
Long Black Veil
Shenandoah
Down in the Valley
Tom Dooley
the one about “the fox went out on a chilly night”
and a bunch of strange stuff my mother (now 97) taught me:
Mighty Like a Rose (definitely not fitting to my pink and blond baby girl)
When You and I were Young, Maggie
Mein Herr, being a trumpeter, knew zero lyrics and had to make them up (which he was not good at) or hum.
“500 Hats,” by Tom Smith.