What Italy tickets/passes should we purchase before travelling?

There are huge discounts for train tickets on trenitalia.com that are available starting four months before the desired travel date. Beyond that, I usually wait to arrive to buy transit passes, museum passes, etc.

It depends on what you want to do. If you wish to take tours these should be booked in advance. If you are traveling by train and know the dates of travel you can book these in advance and save a ton of money. Your question is a little vague. You'll get more precise comments if you tell us what you want to see and do. Donna

Might want to consider reserving the "underground tour" of the Coliseum in Rome.

For Rome: The Vatican, pre-purchase will cut down on waiting in line. The Borghese - all entrances must be pre-purchased.
When you arrive in Rome: The Roma Pass. Good for museums, historic sites and public transport. Available all over the city at tabacs & newsstands. Most sites have separate Roma Pass entrances and you will waltz by hundreds of line standers and enter without a wait.

I think it depends on when you are going to visit- some months are more important to book ahead- Also it depends on your own style of traveling.. personally I like to book things like train tickets ahead of time-save money and puts some guidelines to my days- Tickets to get into certain sites are important if you are visiting during a particularly busy time-this saves time waiting in a line etc- also if there are attractions, museums or must sees on your list this insures that you will get in instead of taking a risk of not getting into a particular place.
Hope this helps..

Florence: Book tickets for the Accademia Gallery and the Uffizi Gallery in advance. Lines can be four hours long. Or buy a 3-day Firenze Card which covers the Accademia, the Uffizi, and other major museums plus bus transportation.

In Rome you can buy the Roma pass at many hotels. It will allow you to skip the long line at the Coloseum which is to buy tickets and move over to the left for the short entry line. The pass is good for several other sites as well as bus transportation I believe. In Florence to see the David at The Academia you will want a reservation and prepaid tickets, search online or have your hotel book it for you. The line is very long otherwise and you will see some very frustrated tourists who didn't bother to book ahead. These tips and many others are discussed in detail in our host's (Rick Steves) books. Well worth the investment and I recommend tearing out the sections and carrying them with you during the day. Use them for the self guided tours and eating recommendations as well as the many time saving tips. You will undoubtedly run into many others doing the same and I enjoy the shared experiences and camaraderie of my fellow RS travelers.

Be careful expecting the Roma Pass to work too much magic. Remember that it only gets you "free" admission to the first two sites - all the rest are smallish discounts. It does get you "free" bus and local train and Metro use during the three days of validity. It expires at midnight of day three regardless what time you started using it on day one.