For some reason I started researching Shawn Nelson's tank rampage in San Diego in 1995. So I decided to go to the Brazilian newspapers archives and search for tank thefts incident, and found two incidents for my list:
Walter F. Brown incident, 1957
In Mannheim, Germany, 1957, an American 20-year-old soldier named Walter F. Brown wanted to impress his girlfriend. To accomplish so, he decided to steal a tank. He someway managed to do it on an 20-ton tank and drove wildly though the station. With the M47 tank he drove 10 kilometers by camps. Another American officer, concerned about the situation, initiated a pursuit against Brown. He cornered Brown and took him in custody, but at this point he already managed to get into his girlfriend's house. He was sentenced to 2 years in prison.
Source: O soldado quis ver a namorada de tanque
William Thompson incident, 1974
Another American soldier, this time the incident also occurring in Germany (Berlim as the incident location), 21-year-old Thompson stole an 50-ton tank and drove through the German Democratic Republic border, surprising Communists guards. Police officers were scared when Thompson turned the tank's roof and threatened the Soviets and Germans soldiers, though no shot was fired from the tank. He was being pursued by 15 vehicles and destroyed objects. Thompson then surrendered.
Source: Soldado americano rouba tanque e invade Berlim
There's also video footage from Thompson's rampage: A tank runs amok