The most famous Italian tongue twister is probably the following:
Sopra la panca la capra campa, sotto la panca la capra crepa.
Above the bench, the goat lives, under the bench, the goat dies.
Tongue twisters are made up to be a pronunciation challenge, and not (as in the case of proverbs) to have a meaning. No profound life lesson can be found in the above, not even for goats.
Here's another one:
Trentatre' trentini entrarono a Trento tutti i trentatre' trotterellando.
Thirty-three people from Trentino entered Trento all thirty-three trotting along.
Again, do not seek any insight into the Trentino region and its inhabitants because of the above.
Here's another I used to say as a kid (and I still know by heart):
Apelle, figlio d'Apollo, fece una palla di pelle di pollo, tutti i pesci venirono a galla per vedere la palla di pelle di pollo che fece Apelle, figlio d'Apollo...
Apelles, son of Apollo, made a ball of chicken skin, all the fish rose to the surface to see the ball of chicken skin made by Apelles, son of Apollo...
Apelles was not the son of Apollo, he was a painter. I also strongly suspect that he did not play around with chicken skin, and that Greek fish took no interest in his activities.
Want to know more Italian tongue twisters? Go to the Wiki-quote entry for scioglilingua italiani.