It's the best time of the year weather wise, as far as I'm concerned. It was my preferred period for going to visit Florence every year prior to 2010 (then new job requirements made it difficult for me to go at that time). Between living in Italy and visiting from the US I can say that I have spent almost fifty 'Mays' in Italy in my lifetime.
Temps are 70s/low 80s F during the day, and 60s in the early mornings and evenings. Obviously generally warmer at the end of the month than at the beginning. There are some odd years when it is rainier (and/or cooler) than usual, and some other odd years when it's as hot as July (generally toward the very end of the month when it happens), but statistically the weather is likely to be great at the time you plan to go. The big bonus is the longer days compared to the fall, as the sun sets late at this time.
In terms of crowds, art cities (Florence, Venice, Rome, etc.) are crowded with tourists. Resort areas on the coast, mountains, or lakes are not (except for weekends, if the weather is very warm).