My husband and I have been told that rail transportation exists between countries in Europe.
We are planning to visit Bern, Venice, Rome from Munich Germany. Does such a rail transport system exist between these countries? Eurail maybe?

The European rail system is excellent and extensive. Try http://www.raileurope.com

The German rail site www.bahn.de gives timetable information in English for the journeys you want.

To my knowledge, there is no rail system named
"Eurail." This is simply a brand name of a discount
pass that can be used on many European countries'
national rail networks, but there is no "Eurail"
railroad. There is a French National Rail System
(SNCF), German, Italian, etc. And trains and
routes are coordinated between countries so you
can easily travel from one to another.

Your best bet for this itinerary might be a Europass, not to be confused with a Eurailpass. I don't have current rates, but in '97 a twin 1st class (for two people always travelling together) was $253 ea. for 5 days in 2 months. Extra days can be added @ $33.50 per day. This pass is good for travel in France, Germany, Switzerland, Italy and Spain. Rail travel in Europe can be a little confusing, some trains require supplements (the very high speed trains), some require reservations. For experienced help, call Budget Europe Travel Service, they have people that travel Europe each year and so are prett up-to-date. They are at 1.800.441.2387 X80. Rail is a wonderful way to travel in Europe.

For international rail travel in Europe check http://www.bahn.de/home_e/f-engl.htm which contains the European timetable, showing regional, inter-region, intercity and eurocity connections all over Europe