How widespread those are depends very much on the country. There are some in which most people haven't seen a laundromat in their life outside of American movies.
I didn't say that they are unique to America. And yes, many countries do have them in abundance. Many others do not, or they are rare enough that you might not have one nearby.
I'm from Russia originally and the first time I have ever seen one outside of a movie was when I moved to Canada. Russia does have them, but, generally speaking, only in large cities.