When I had children, I continued the custom. Robert Louis Stephenson was a favorite and some of the rhymes that I had loved came back for the second time. Winnie the Pooh was a favorite of mine and theirs. I still love the rollicking joy of the Pokey Little Puppy. I was never able to fine one of the poems I loved when I was little to share with them even though I looked through all the children's collections I could find. I remembered it as "The Sheep Song," but that was incorrect.
The Internet is a wonderful resource. With a little research I found "The Sleepy Song" and it helped me call back the blessing of my mother's voice, the comfort of warmth and peace at bedtime, and the love of those who laughed and loved me when I was four. You will find it reprinted below.
Read to your children. It may be a blessing to them all their lives.