Asklemmy

Since capitalism has been the most common economic system since its rise in the 19th century, it's the majority of the countries that have fallen since then, and a bunch of sovereign states before. It's a large (and probably contested, based on definitions) list. I am confident, for one example, to list the British Empire in the 1800s onward which embraced free trade, liberalism and a market economy [wikipedia]. It's not a country, but a capitalist empire and the "first global economic superpower" that shrank from this in 1921 to these current 14 overseas territories. I realize it's not strictly a country but it demonstrates the point of a big capitalist system falling. If you don't consider fascism to be capitalist (debatable based on definitions: socialists generally consider them capitalist), then I believe liberal Kingdom of Italy and the Weimar Republic (Germany) before the '20/'30s count too.

A different (IMO better) question is whether capitalism itself was the cause, or how it influenced their downfall. And that's obviously a complex question. Merely being capitalist/socialist/etc. and falling (even for economic reasons) isn't a solid reason to abandon those economic theories, especially when these systems were new and being trialed for the first times.