Well, there are thousands upon thousands of languages in the world, and I'm only familiar with a couple, so I can't really say how many use multiple negation. I know that Romance languages typically do use double negatives, but Germanic languages typically don't. (Though English used multiple negatives at least until Shakespeare's time, so I wonder if other Germanic languages lost it, or if we picked it up somewhere.) And
according to this, many Slavic languages use double negatives.
So where does the English rule come from? From a bunch of grammarians who decided that language had to be logical. They figured that two negatives make a positive, even though in English, two negatives generally make something
more negative (I guess they thought that you multiply them, when really they should have been adding). But the rule has been around for long enough that it's not going to go anywhere anytime soon.