A couple years ago, a coworker who had a one year old son mentioned she was looking for some good songs she could sing to him. I recommended “Godspeed” by the Dixie Chicks because I sang it to my brother when he was little. The lyrics have religious references but they can easily be substituted for nonreligious words if needed. It is a really beautiful song.

Dixie Chicks- Godspeed 

I also sang my brother the “Skinnamarink” song from Sharon, Louis and Bram’s Elephant Show. I hadn’t seen the show since I was five years old but I could still remember the words and the accompanying hand gestures:

Skinnamarink