Rail Pass and Regionale Trains

Yes, that's the case (within the validity period of your Pass, of course). Be sure your Pass is validated before first use and BE SURE that the train you're boarding is in fact a Regionale. If it's an InterCity or other type (with compulsory reservations), you'll probably be fined if you don't have a seat reservation.

That is true on both Regionale and Regionale Veloce but nothing higher as Ken said.

Big exception though - the pass is not valid on certain specific trains - such as Leonardo Express, Trenord out of Milano, Circumvesuviana, and some private routes in the south of Italy.

But that is a very small subset of Italian Regionale trains.

Whether medium-speed InterCity and EuroCity trains require reservation depends upon the route and country, just as the rule also varies for faster trains. For instance, you rarely need reservations for daytime trains in Germany, Austria, Switzerland, or much of Eastern Europe. The best way to get that info is to look up train schedules through DB online or their DB Navigator mobile app. Eurail also provides an app for you, which doesn't require internet access. See also Reservations and Using Your Rail Pass. Any "private train" exceptions that are likely to come up are listed on each single-country page at http://www.ricksteves.com/travel-tips/transportation/trains, such as for Italy and Switzerland.

One note worth mentioning, the above is good advice if you have the continuous days Global pass. If you have the flexi-pass, I would look at the cost of travel before using a travel day on a pass. In Italy, regional trains are relatively cheap and distances somewhat short, making it difficult to justify using a flex day.

Have you run the numbers to make sure that a Global Pass makes financial sense? In Italy, rail passes virtually always cost more than point-to-point tickets.