To be honest. . . Every child is different. Some like humming more than singing. Others would prefer a noise. All ages are different, but mine would prefer humming more than singing. I hum all of the nursery rhymes at least once to get them to sleep.
It's got to be "Oh Mr Sun, Sun, Mr Golden Sun please shine down on me. I sing this to my little pre-schooler in the morning and it always puts a smile on her face. She finds it hard to get going in the mornings (like me!) so we sing this on our journey to playschool and she arrives there in good form. I have posted a video of this song on my blog.
I use to sing all sorts of children's songs, hymns and lullabies to my boys to get them to clam down at night, but lately, the song that they love to hear is Enter Sandman: "Say your prayers, little one. Don't forget my son, to include everyone..."
You should see the smiles on their faces as they grab their pillows tight and pretend to sleep with one eye open.