My mom used to sing me, "You Are My Sunshine," as a lullaby when I was a baby. While I do tear up whenever I heard the song (which is extremely rare) I wouldn't say it's something I'd put on my iPod.
Meanwhile, my dad's idea of lullabies were "Mother," and "Another Brick in the Wall (Pts. 1-3)," by Pink Floyd, "Big Yellow Taxi," by Joni Mitchell, and numerous songs by Yes!, Peter Gabriel, and Television, all bands and artists I almost worship today.
Also, as I saw a recent poster mentioning his famous father of Blood, Sweat & Tears, I'd just like to mention my father's best friend and my drum teacher, played guitar in the band Winter Hours, an alternative rock group of the early 90's. They opened for R.E.M, and were very popular locally, and still maintain a somewhat small but strong following, despite their age and their lead singer passing away due to drug overdose.