My mother used to sing "Song to Celia" to me, as well as "Today while the blossom still clings to the vine" (I'm not sure what the actual title is). Dad sang "Rockabye Sweet Baby James", The Grateful Dead's "Casey Jones" and a quiet,slow version of America's "Sister Golden Hair". Dad's a bass, and always sang all of those an octave lower than the original...it may very well have just been the rumbling bass notes that put me to sleep.
I've used "Over the Hills and Far Away," "Unforgettable," and "Secure Yourself" (The Indigo Girls) as lullabies for my baby cousins.