If we're eating it the same day we buy it, we leave it out. If we're having it the next day, we put it in the refrigerator, and then pull it out the morning we plan to eat it. Most of my Florentine friends think refrigerating it is heresy.

I accidentally left some overnight w/o the water.. the outer surface tends to dry out & the texture becomes a bit more chewy, but definitely edible..

Good question (since it's always best if you leave it out!). Fresh mozzarella di bufala can be left out on the counter for about a day -- in the water it comes in -- after which you want to put it in the fridge. Funky mozzarella won't kill you, it just won't taste as good -- that's for sure.