Until recently the state-run museums and archeological sites in Italy granted free admission to minors who came from European Union countries; however, minors visiting from non-EU member countries were charged admission. This included such famous sites as the Uffizi Gallery in Florence, the Colosseum in Rome, the National Archeological Museum in Naples and many more. At 15 Euros or more per admission that could put quite a dent in a family’s budget when traveling with children, or probably even more of a dent for minors traveling alone (the EU defines a minor as being under age 18). So this is welcome news for those coming from the U.K., Australia, U.S. or other countries outside the European Union.
Note that this does not apply to private museums (notably such places as the Vatican Museums and Sistine Chapel) which will continue to charge admission for minors.
For a complete list of state-owned museums check out this page on Wikipedia to help you in your travel plans.