The City of Fountains... but are they drinkable? Or if you prefer proper words, potable?
Yes, Rome's tap water is safe to drink.
97% of Rome's tap water is spring water transported by the the Peschieria-Capore aqueduct.
Likewise, you might have seen all of the fountains around town that are about waist-high with a curved spout. These are called nasoni, named after the "nose" the water fountains have. These are also totally safe to drink from, as they are also pumping out fresh spring water transported into the city.
The water that isn't used (as these fountains are perpetually flowing) is typically piped away for agricultural use.
I don't recommend drinking for Rome's larger fountains (like the Trevi Fountain). While this is also spring water, it's been recycled, so there's no telling what's in the water.
The City of Rome discourages drinking from some of the more famous fountains with signs that read acqua non potabile. If the water is safe to drink, there's usually a sign that says acqua potabile.
For the seasoned travelers, you might notice that the top of the nose on the nasoni has a small hole. IF you plug up the larger hole with you finger or a palm, water will shoot out of this smaller hole, arcing through the air. That's on purpose! It's designed to be used as a water fountain so you don't have to bend over and drop your glasses (like me) into the puddle below.