What year did the Romans invade germany?

While there was a tendency for the Romans to regard the Rhine River as a natural frontier, incursions by the Germanic tribes into Gaul and the Low Countries caused them to periodically cross the river on punitive expeditions. These generally had a limited success, however in 9 CE an entire Roman army under Varus was ambushed in dense woods at Teutobergerwald and wiped out. Germany was invaded again several times, one recapturing Varus' lost eagles. It was never fully subdued, nor did the Romans really intend to occupy Germania permanently, as it would have left them with an open indefensible frontier with eastern Europe and tied down too many legions for no real gain as it was not a rich country.