I remember Mum singing "Song To Celia" and lots of Simon and Garfunkel. She was also fond of one that I don't know the title to...
"Today while the blossom
still clings to the vine
I'll taste your strawberries
I'll drink your sweet wine"

Can't remember any more of it than that off the top of my head.
I also recall singing "Misty Moisty Morning" with Mum in the car--it was -years- before I realized it wasn't a typical children's song in this century. *grins*
Dad used to sing mostly "southern rock" stuff and play his guitar for me when I was little. This resulted in some amusing moments, like my translation of the Grateful Dead as "Ridin' that train, Hi I'm okay."