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I don't know if this really answers the OP's question or not but from what I've researched it seems easier for foreigners to join the U.S. military than for Americans to join some other country's military. I got forced out of the U.S. military via BRAC last decade. Basically long story short, they closed a lot of bases or changed the mission(s) of the base(s) and a lot of people got screwed because of it and lost their jobs. I loved being in the military and have missed it pretty much everyday since I separated. I looked into joining foreign militaries as a U.S. citizen and it's surprisingly quite difficult. The only one that seems to readily accept Americans is the FFL but honestly that's not one I'd be interested in joining. I was interested in serving the UK, Australia, Canada etc. so there wouldn't be a language barrier. Forget it, they don't want Americans.
I know for a fact that you can serve in other countries' militaries, at least ones that are friendly to the USA. Many Americans have served in the Israeli Army and come back with no problem. I'm going to guess that it's also OK to join any NATO military.
Common sense would tell me that you're guaranteed to go to jail, or at least be "detained" for an extended period of time if you join the Iranian or North Korean Army. And you're definitely screwed if you belong to an Army that ends up fighting US forces.