DW and I lived in Italy all of 2006, here is my advice: Rome is at least 2-3 days in itself. Florence is wonderful and can possibly be done in one rushed day or more likely two.
Always call ahead for reservations to the most popular museums and art galleries (The Last Supper has a waiting list most of the time) Venice is nice but as one other person posted it can be done in one day.
All these cities are tourist traps so I would not recommend buying souvenirs in the cities, find smaller, out of the way towns to stop in and get your souvenirs.
Lastly, Italy is best enjoyed slowly. Don't try to rush through too much in a week. Pick one or two cities and take your time. Find the small out of the way places and restaurants, they are the best Italy has to offer.
Some of our favorite places were little known: Casole d'Elsa; Lago di Como; Montepulciano; Lago Di Garda; Siena; Cinque Terre.
"Those who think it cannot be done, need to stay out of the way of those of us doing it."