The Itsy Bitsy Spider Song Kids will enjoy this classic nursery rhyme song of the itsy bitsy spider. Watch the spider battle the elements as it strives to climb up the water down spout. Lyrics: The Itsy Bitsy Spider climbed up the water spout Down came the rain and washed the spider out Up came the sun and dried up all the rain and the Itsy Bitsy Spider went up the spout again.