Luggage and bags:
Good luggage with wheels for the cobblestone. And extra compact bag for bringing home souveniers.
Clothing/Shoes/Weather Gear: Shoes! Good Shoes. There is lots of cobblestone in Rome. Fabulous scarf for those chilly nights. Pay attention to how the locals wear them. So chic.
Toiletries and Medical Supplies: Sunscreen, Hat
Photo Equipment: Good camera batteries and film. So much cheaper and easier to find at home.
Miscellaneous: Washcloth. The hotels in Italy don't have them. In fact they only have one large bath towel then several hand towels that are made out of the same type of cloth that I would compare to cloth napkins. This was the case for the three hotels where we stayed in Italy. Also, bring a good language guide.
Definitely bring a couple pairs of comfortable shoes. I generally wear one pair during the day and the second in the evening to give my feet a break. The next day, I wear the second pair all day and the first pair all evening.
Miscellaneous: Even though you are in the city, it is very wise to wear sunscreen in Rome in the summer. Places like the Forum have very little shade and can be very hot during the day.