Theoretical cross-continent road trip

[Fev]

It's always been a dream of mine to take a car of mine across America or Europe. Maybe not in my Escort as it's too unreliable but in my old Falcon all i wanted to do was drive the alps of Switzerland etc.
How easy is such a thing to do? I'm not talking about the shipping and customs, or getting to Europe but to do cross-country driving. Do i need to change my number plates from Australian to something else?

Scenario: My brand new FG F6 Typhoon is fully registered in Australia and I have an international license. If I shipped it to Rome to drive from Italy to Sweden would i need Italian, Swiss, German, Danish and Swedish registrations?

Same goes for America, if i were to take my Australian plated/registered car to America, would i be allowed to drive on their roads legally from one side to the other?
It just seem's odd that i would be allowed to drive through Europe or the USA on Australian registration if it's so, or is there special plate and registration plate i can get?