As a general rule, countries that are party to the 1961 Hague Convention Abolishing the Requirement of Legalisation for Foreign Public Documents require an apostille on documents that qualify as Australian public documents.
These countries include Italy, Croatia, Greece, the Netherlands, Israel, South Korea and many others. A full list of countries that are party to this convention can be found at the Hague Conference on Private International Law website.
Some countries will accept an apostille for certain types of documents, and many require an original government document to have been issued within 3 months of the apostille being affixed. This is especially the case in relation to birth and marriage certificates issued by the State Registry of Births, Deaths and Marriages (BDM).
You must check the foreign requirements. Often, it is the original BDM certificate that requires an apostille, not a translation or copy of it.