Is it necessary to get reservations on all train trips in Italy ? Seven years ago while traveling in Italy with my daughter through Cinque Terre, Milan and Lake Como by train we went reservation-less. No problem. This trip I am going from Cinque Terre to Venice, Venice to Florence and then Florence to Rome. Do I need tickets for all of those legs? We have Global Eurail passes , already purchased.
All trains in Italy except for the Regionale trains require a reservation and there is an extra charge for the seat reservations for pass holders. If you do not have a seat reservation the fine is substantial and immediate. So don't risk it. Regionale trains are open seating so you can get off and on at will with a pass. A global pass is not cost effective in Italy.
To add to Frank's reply, you should be able to get your seat reservations from the ticket machines, so you won't have to wait in the lines (often long at large stations). But as he says, don't just hop on a fast (non-regional) train without the reservation for THAT specific train, as there will be a heavy fine.
Of the routes you mentioned, Venice to Florence and Florence to Rome are on fast trains with no changes. Cinque Terre to Venice is on a mixture of regional and fast trains, and you will change trains several times. You can look at Trenitalia's website to see your options on that route (click the British flag on the upper right to change to English): http://www.trenitalia.com/