The short answer to the questions is always the same: You can't take it with you!
A bilateral agreement between the United Sates and Italy, which came into effect on January 23, 2001, when details were published in the US Federal Register, prevents the importation to the US of almost all artifacts from Italy representing the Pre-Classical, Classical, and Imperial Roman periods ranging in date approximately from the 9th century BC to the 4th century AD. The only exceptions are items that are accompanied by appropriate export certificates issued by the Government of the Republic of Italy or by documentation demonstrating that the articles left Italy prior to January 23, 2001.
The catalog of items covered by the import regulations is very detailed, and it is clearly designed to include every kind of artifact that was made in the time period: stone sculpture, metal sculpture, metal vessels, metal ornaments, weapons, armor, inscribed or decorated sheet metal, ceramic sculpture and vessels, glass architectural elements and sculpture, and wall paintings. The regulations, including a list of categories that need documentation for import, can be found at the US State Department link to the appropriate Federal Register entry: http://exchanges.state.gov/education/culprop/it01fr01.txt.
And just because a category of items might not appear in the list, it doesn't mean your home free -- the list is exemplary and not necessarily comprehensive.
There's another thing to note: the fact that you got the item in Italy, rather than where it was made, is the controlling factor. The controls are specifically on items imported "from Italy" and not only on items made in Italy. That means that the many kinds of Mediterranean items that the ancient Romans originally got from outside of Italy are also covered by the controls. Some kinds of Greek pottery that can't be imported are specifically mentioned in the Federal Regulations list, so it would be wise to have proper Greek documentation on any such items you may have purchased in Greece.
Note also that there are no apparent exemptions for items that you may own from previous trips to Italy -- if you brought something Roman with you when you came to Italy, it appears to fall under the regulations.
Slipping a few items into household-goods shipments is definitely not a good idea. The importation is still illegal and criminal intent wouldn't be too hard to prove. The consequences of getting caught in such shenanigans can be expensive and devastating to lives and careers. It's just not worth it.
Finally, a 2000-year-old artifact is really nothing but a "trophy" that doesn't even prove that you've been here. A good photo display -- you standing in the ruins in the forum, for example -- gives you much better "braggin' rights." If you must have something tangible, good copies of small artifacts are available at all of Rome's museums and at the Commissary Gift Shop. Larger statuary can be found in shops in the streets between the Gesu church and the Pantheon and at marble works on the outskirts of town. And you don't even have to tell your friends back home that they are fakes.
Federal Register: "Import Restrictions Imposed on Archaeological Material Originating in Italy and Representing the Pre-Classical, Classical, and Imperial Roman Periods" http://exchanges.state.gov/education/culprop/it01fr01.txt
State Department "US Protection" Italy page: http://exchanges.state.gov/education/culprop/itfact.html
The Embassy notice that some of you must have missed: http://www.usembassy.it/file2001_01/alia/a1012206.htm
"Fighting Illicit Traffic of Cultural Property", from ICOM: http://www.icom.org/traffic.html
UNESCO and UNIDROIT conventions: http://www.icom.org/convention.html
The most famous case -- the golden Steinhardt Phiale: http://www.archaeology.org/online/news/phiale.html
PS: A "Trophy" (Latin "Tropaeum") among
the ancients, was a pile of arms taken from a vanquished enemy, raised
on the field of battle by the conquerors; also, the representation of such
a pile in marble, on medals and the like. In earlier times, according
to some sources, trophies were trees planted in conspicuous places of the
conquered provinces, and hung with the spoils of the enemy, in memory of
the victory. By extension a trophy became anything you brought back
as proof of participation in a foreign campaign.