4. Sylvester Stallone vs. Communism

Background
My original idea here was Rocky Balboa vs. Communism but then it was brought to my attention that John Rambo was also dedicated to wiping out the Red Menace. So it became very clear that Sly Stallone was obsessed with single-handedly destroying communism.

Why This is a Great Rivalry
Do I really need to explain? The ultimate action star of the 1980's versus the quintessentially evil political ideology of the 1980's.

John Rambo started things off by softening up the enemy, drawing First Blood:

http://www.youtube.com/watch?v=lc0BH3mK5Ek

Then Rocky Balboa ended the Cold War with his 15th round knockout of Ivan Drago. Once Drago went down in Moscow, there was no longer any hope for the Soviets - the Cold War was over:

http://www.youtube.com/watch?v=QMpSDwlGrKA&mode=related&search=