Besides the allied countries who are in Europe themselves; I think you may be asking mostly about US presence in Europe?

One could make the argument that the military presence continues to this day. [Ramstein] (http://www.ramstein.af.mil) Airforce Base was built in the decade following the Second World War and remains in use by the US Airforce as well as NATO command.

The US kept troops/advisors in Europe to help rebuild after the war and as part of the European Recovery Program (or Marshall Plan). This post-war building boom was funded by the United States and was intended to help European economic recovery and infrastructure expansion.

The aftermath of the Second World War is the Cold War; so arguably any legacy of hostility was muted by the division of Germany and brinksmanship of the US and Soviets.

U.S. military presence in Germany and western Europe has been ongoing since the end of World War II, so technically the Allied occupation never ended. Basically, Allied occupation in western Europe just transformed into the foundation for NATO.

In eastern Europe, of course, the Soviet Union's post-war occupation lasted until 1989 when communism fell. Austria was jointly occupied by the U.S.S.R. and the western powers until 1955, when both pulled out on the condition that Austria would be neutral in the Cold War.