are reservations necessary for train travel

With discount fares through trenitalia.com you can save a LOT of money getting your tickets in advance. Hundreds of dollars. Srsly. More info here: Buying Trenitalia tickets

One suggestion - I had a lot of trouble with the trenitalia website, so when I finally got it to work, to reserve two train trips, I quickly bought them. But then I saw in the confirmation email that they assigned seats to us, and they weren't necessarily together. So if you do it online, take the time to seats, if that's an option. Also, it will save you some money even to buy the tickets a few days ahead, so when you arrive in one city, you could buy the tickets for when you'll be leaving the city. Oh, one final thing. Make sure you have your credit card's PIN number - I'd suggest calling and asking. I put my credit card in an ATM before the trip, and entered a PIN, and got far enough where it asked me if I wanted cash, but then didn't get cash (because I didn't want the fees). But that PIN didn't work in the train ticket machines in Italy. I had to use my bank debit card. Luckily I had checked ahead of time and knew I'd have no foreign transaction fees (TD Bank).

FWIW, we never had a problem using our credit card without a PIN at the train ticket machines.

sue, YES, reservations ARE compulsory for travel on some trains in Italy. This will depend on the type of train that's operating on the route you're travelling. ALL of the fast Freccia trains require reservations, while the slower Regionale trains do not. Travel on a particular route may involve riding on both types of trains. If riding Regionale trains, DO NOT forget to validate your ticket prior to boarding the train, or you'll risk hefty fines which will be collected on the spot (and they're not cheap)!!! For tickets on the fast trains, it's possible to save some money by pre-booking on the internet. However, as some have mentioned, the Trenitalia website is not always "user friendly" so this can be "hit & miss". Also, when the cheaper tickets sell out, the prices increase. Trains rarely ever sell out, so I usually just buy tickets when I arrive in Italy, typically a few days before I'll be travelling. Tickets can be bought either at staffed windows or from the automated Kiosks. One other point to mention is that many cities have more than one station, so you'll need to know the correct station to specify when you buy your tickets. For example, for the trip to Venice, the appropriate station is Venezia Santa Lucia. For the trip to the Cinque Terre, you'll need to specify which of the five towns you want to arrive at. Happy travels!

Looking at your travel agenda, many of your train journeys will be on Regionale trains. No seat reservations permitted. Assisi/Lucca, Lucca/CT and CT/Florence are mostly on Regionales. For CT/Florence, you might get lucky on the few Intercity and high-speed trains that make part of the run. On the remainder of your train journeys, you actually have a choice between a Regionale or a high-speed. With a few circumstances notwithstanding, you can't buy the tickets for a Regionale train until you get within 7 days from the date of travel. For the high-speeds, you can book them now. If you buy now, you can get some great fares on the high-speeds if you are willing to lock in a specifc travel date and travel time with a non-refundable and non-exchangeable ticket.

It may be helpful to visit a local travel agency once you get to Milan or Venice. Rick often recommends certain agencies in his books. These recommended agencies usually have English speaking staff members available to answer questions and help you book the tickets you need. They may know of deals that aren't listed on websites. Last year, we had a group of 7 traveling so it is worth a certain "peace of mind" to have the tickets all purchased through a travel agent. If I mess up at a kiosk and it's just meno big deal. But with a fairly large group, I feel better getting the tickets from a professional in the business.