My wife and I just spent three weeks there.
6 days in Rome, 4 days in Venice, and 6 days in Florence.
You will need at least 2-3 days to see most of the "touristy" stuff in Rome. Plan for a full day to see the vatican/vatican museum. Another day to see colloseum, forum, and the other things like spanish steps.
Venice can be done in 1-2 days. There really isn;t much t see/do there besides san marco square with the doges palace and st. marks basillica. Beyond that it is mostly just walking around.
We aren't really in to art, so we didn't do much in the city of florence besides see the duomo. We spent the rest of the time in florence going out into the countryside horseback riding, touring vineyards, and visiting the smaller cities like sienna, san gimignano, and pisa.
Overall, my favorite things were sienna/san gimignano, touring the countryside, and walking the streets of venice.
Florence itself stinks like exhaust fumes. My guess is because it sits between some mountains so none of the smog can escape. Rome is a dirty city and very hectic, but once you get used to it it's pretty nice. The subway system is great for getting around. DONT DRIVE!
Also, if you want to go to venice, try not to go on a weekend. It will be so packed you will be literally elbow to elbow in the entire city.
edit: If you have any questions about any of those cities, what to do, where to stay, where to eat, or want and pictures of anything, let me know.