The lyrics of the song go something like this:
The itsy bitsy spider climbed up the water spout.
Down came the rain, and washed the spider out.
Out came the sun, and dried up all the rain,
And the itsy bitsy spider went up the spout again.
So, the protagonist of the song is a spider, which is a surprising choice given arachnids' bad reputations. The only other exception to the spider-as-antagonist rule that I can think of is Charlotte's Web, which is devastating in its own right as a book that will make you cry when a spider dies, and--here's the kicker--be happy that it laid eggs and had lots of little spider babies! "Hooray," the child reader thinks, "now the barn is full of brown recluse spawn! Now that cool rat will have some new friends to play with! ...Mmm, I bet Wilbur would make a pretty radiant BLT."
The itsy-bitsy spider of the song is an excellent exemplar of the tragic hero. He shows determination and resolve in his quest to climb the water spout, but fails through his own frailty and the cruel intervention of the gods (I mean come on, how convenient was that sudden downpour? I'm looking at you, Zeus). He is brought low through these external forces (Have you ever seen what happens to a wet spider?) and yet continues in his Sisyphean pursuit. The song's preschool-age audience, however, rarely appreciate the enormity of such peripeteia, and continue to laugh and wiggle their fingers in glee.
If itsy-bitsy spiders climb up your spout again, 1-800-TERMINIX.
Fisher Price: Itsy-Bitsy Spider