In theory, official galateo (etiquette) rules dictate that pizza should always be eaten with fork and knife only, except when it's “pizza al taglio”, i.e. “by the slice”, which is meant as street food and can be eaten directly with hands.
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In Italy you can eat a pizza with cutlery or directly with your hands. However, according to etiquette, you have to eat it with cutlery only if it's a whole pizza (e.g. as they serve it in a restaurant), while you can eat sliced pizza with your hands (e.g. as they serve it in the street food tradition).