Look at a very big (but not terribly up to date) picture of Bikes on Trains. (Special thanks to Massimo Nicolodi.)
to the Trento Bike Pages.
See similar information concerning France.
You can carry your bike with you on every Italian train, except those labeled "P" ("Pendolino", sort of a German ICE), provided you
If you're traveling in a biggish group, it is necessary or at least advisable to check with the station of departure in advance. Some trains cannot accommodate easily more than half a dozen bikes at a time.
All you have to do to take your bike with you on an Italian train is to buy a special ticket, besides the regular ticket for you. This costs 5000Lire, that is, approximately 5DM or less than 4.00$ (price and exchange rate as of October 1994). On beginning the trip, you have to stamp your ticket (which carries no date) on both sides at the machines you find in the stations. You are now entitled to free travel for your bike for 24 hours, no matter how many trains you take.
This information is extracted from the Official Timetable of the Italian Railways (Winter 94/95). I have used the latter option a number of times around Trento, and it works well.