The Cold War can be blamed for starting many other wars. The two biggest of these wars were the Korean War and the Vietnam War. In both cases, the wars came about because of countries being split between communist parts (North Vietnam and North Korea) and non-communist parts. In both cases, the communist part was trying to unify the country by conquering the non-communist part. There was also the war in Afghanistan that came about after the Soviets invaded that country in 1979 to prop up its communist government.
Outside of this, there were several civil wars that were started at least in part by the Cold War. One of the most notable of these was Angolan Civil War, which was fought between communist and non-communist forces in the time after Angola became independent from Portugal.