I’m not a parent, but I’ve sung babies to sleep with Loudon Wainwright’s “Lullaby”.
You Are My Sunshine, Close To You by the Carpenters and Can’t Take My Eyes Off of You by Frankie Vallie
AC/DC’s*Highway To Hell*
Brahms’ Lullaby with lyrics by Cyril Sneer: “Go To Sleep, Close Your Eyes, May Your Bank Interest Rise…”
and
Cocteau Twins’ For Phoebe Still A Baby (I sound nothing like that, but the tune and glossolalia is quite sleep-inducing, even when it’s me croaking it)
Crikey its been a few years, the rug rats are nearly adults.
I do remember an adult asking my 5 yr old son who his favourite music group was and he said “Black Sabbath”. Then he beamed a rascally smile at me. :smack:
So much for the Fleetwood Mac and Carly Simon normally playing on the car stereo.
Very few of my lullabies are traditional lullabies. But if we’re talking “bedtime songs”:
“Everything’s Alright” from Jesus Christ Superstar (I leave out the argument) and “All the Pretty Little Ponies” were my son’s favorite. “Personal Jesus” was a close third.
My daughter was partial to “Too-Ra-Loo-Ra-Loo-Ral (That’s an Irish Lullaby)” and “We Love You, Conrad” from Bye, Bye Birdie, with her name in place of Conrad’s. The later was always the final song we sang her to bed with, and it became Pavlovian. I taught it to her babysitters and her grandmothers, and they were able to get her to sleep immediately, even in a strange place, with that song. You should have seen the look on her face the first time she watched Bye, Bye Birdie and heard “her” song! 
My personal favorite has always been “Part of Your World” from Little Mermaid, because it’s so dang fun to sing.
The Beatles “Good Night”. I’ve sung it to my grandson since he was a baby. He’s now 13 and sometimes still requests I sing it to him. He was very surprised when he heard Ringo sing it, as he thought I’d written it just for him.
I used to sing the acoustic version of Clapton’s Layla to my daughter, substituting her name for Layla. For my son there was a nonsense song I wrote myself called Chicken & Grits.
Both kids remember their songs to this day.
This was well before the release of Go The Fuck To Sleep, otherwise things may have ended differently.
Here are my Mom’s Top Hits, and I always sang them in this order —
Edelweiss — soft and cheerful to start them out
My Old Kentucky Home — goes nicely after the German-themed preceding song
Somewhere Over the Rainbow — very much a standard in my house
Surrey with the Fringe on Top — this makes a surprisingly terrific lullaby; it ends with nodding and sleeping.
When Christmas rolled around, I always sang Christmas carols, with Sleigh Ride, Walking in a Winter Wonderland, O Little Town of Bethlehem, and Silent Night being their favorites.
Nope, it was Taxi. She had no idea what it was about, but loved “where are you going to, my lady blue?”
Celtling’s favorite is Dun do Shuile, second favorite is Faoiseamh a Gheobhadsa (Colm O’Snodaigh’s tune, which I can’t find a link for), then “Feed the Birds” followed closely by “Sweet Baby James”
I had to laugh when my wife started it, but I do it now too.
Adventure Time : Baby’s building a tower to space.
I do hope that when he grows up, he doesn’t take the lyrics to heart.
That, and “Soft Kitty” from Big Bang Theory.
I used a couple. Milord by Edith Piaf - I had learned it in high school French class, and it just jumps into my head sometimes and sticks there. No idea why I started singing it to my son, but he liked it.
But the main one- Rock Of Ages. My godmother started it when he was a newborn, and it worked so beautifully that I kept it up. Instead of the words we just sing “Na na na naw”. He’s ten now, and we still use it occasionally for soothing purposes.
We used the "In a cottage in the woods; a little old man by the window stood; saw a rabbit hopping by; knocking at his door.
Help me…etc.
But our dau in law improvised her kid’s songs by using the ‘Knick Knack Paddywhack’ song and compoosing her own parts of verses, making the song about their three cats…“This old man, he makes one, he makes knick-knack on his thumb, with a knick-knack, paddywhack, GIVE THE CAT A TREAT, IVANHOE HAS FURRY FEET” etc. for each cat.
When we had to babysit the kids, we used everything we could, including making a tape of us singing a whole bunch of songs – they were calm when listening, but were very slow to sleep.
When they were exceptionally fussy, ‘Hey Jude’ worked better than almost anything, interposed with "one, two, three, four…can I have a little more…five, six, seven, eight, nine, ten…I love you. Altogether now (altogether now), altogether now (altogether now) altogether now (altogether now)…I love you…repeat one hundred times or more as needed.
90% “I Gave My Love a Cherry”
10% “Summertime Rolls” by Jane’s Addiction
These are currently the ones we do on rotation:
Golden Slumbers and Good Night (The Beatles)
Danny Boy
My Bonnie
Waltzing Matilda
Goodnight my Someone (Music Man)
Twinkle Twinkle
La la lu (Lady and the Tramp)
Everything’s Alright (Jesus Christ Superstar)
That was my favorite to sing to my son when he was little.
I wrote a little samba-rhythmed lullaby for Michaela shortly before her first birthday.
Prior to writing that, I’d generally sing her The Dewey Dumpster Song, a love song I had written to her mother back in the 80s, when I was courting her.
I had a song for each of the kids I worked with in Brazil, each their own. One of the boys, who was very, very special to me had a Dutch lullaby called “Suja suja Prikkeltje”.
Suja doesn’t mean anything, pronounced Sue-ya, Prikkeltje means “little prickle” - it’s a lullaby for a porcupine. In the song, Mama Porcupine lists all the things the other animals have that seem impressive, like the parrot’s blue and green feathers and the giraffe’s long neck, but ends each line saying that her baby’s prickles are a great thing too. In the final line she says: “Suja suja Prickly, it’s getting very late, you are the most beautiful porcupine in the world”.
That was his lullaby and he loved it. I wasn’t allowed to sing it to anybody else, not that I would. One night I was singing it to him, and all the other grown ups stood outside the boys’ room listening, and wanted to know what this beautiful love song was about. 
(It was pretty funny when I said “a porcupine”)
Years later, he got someone to help him send me a letter. He’d copied out all the words to the song, which I had written out for him, and at the bottom he wrote: “You can sing it again.”
I can’t though. It’s his.