In many cases they were birthed by the growth of nationalism. The Freikorps operated in Germany and western Europe from the time of Napoleon until the rise of Nazi Germany but their most famous years of operations were as pro-Nationalist pro-Fascist paramilitary organizations who fought in a variety of theaters. Usually their presence was opposition to "communism" but often the reasons they were actually there was to promote a pro-German ideology in nations that would later be considered part of the greater Germania/greater German Reich plan under the Nazis. It's not a coincidence that many of the people who were involved in the Freikorps after WWI ended up in high ranking positions in the Nazi government or in the Nazi party (and this is where much of the original numbers for the SA came from, as Rohm himself had been a Freikorps and militia commander).
These types of forces were used to bolster dictatorships and fascists throughout the 20th century. After WW2 Skorzeny (a famous Nazi commando) set up a group called Paladin that existed mostly to supply mercenary support (usually via ex-Wehrmacht or ex-SS men and advisors) to a variety of nations (usually dictatorships but he also, bizarrely, worked with Mossad). There were also the infamous SS blue division, mercenary troops sent by the authoritarian states who wished to remain neutral in WW2 (Spain and Portugal) but wanted to covertly assist the Nazis in their war against the Communist advance in the Ostfront.
Later you would have the large amount of foreign (usually British and American) troops who fought in the South African border wars and especially in the Rhodesian Bush War. These were politically motivated people, many of them ex-military, who were usually tied up in far right anti-communist circles. Many had come from Vietnam and other conflicts where they had fought communist insurgents and so they transferred their knowledge/skills over to fighting communist insurgents in other countries. You can read the old issues of Soldier of Fortune magazine which broadly covers many of these conflicts while also lionizing the men who fought there as mercenaries (they have a very strong pro-African whites, anti-communist stance and are also, lets say, fantastically embellished).
Mercenaries also were used in support of the communists in many of these conflicts. Vietnam had volunteer brigades raised from neighboring countries with strong Vietnamese ethnic groups. Various South American nations supplied both official and unofficial soldiers to conflicts like Angola and South Africa. The Chinese and USSR often supplied military advisors, training and weapons to a variety of pro-communist revolutions throughout the entire cold war. And the supplies and and training they provided are still in use in many conflicts to this very day (there's a reason the AK47 and PPSH are so common in insurgent circles).
Africa is the major hub of mercenary activity these days and going back into the later years of the Cold War. In central Africa it was and is very common for deposed rulers, exiled generals and the like to run across a border with their remaining troops and then end up fighting in support of a completely different civil war from the one they left. You see this with the relation of the conflicts in Liberia to Rwanda and the Congo, where huge amounts of armed forces have moved from country to country under various banners seeking new conflicts and pillaging targets. In the Congo the Mai-Mai would be a good example of wandering bandits, mercenaries and militias (sometimes or even often they are all of these things and more due to the remote nature of the interior of the DRC).