However, if you take the Nintendo Power comics into account, Mario and Luigi lived in the Mushroom Kingdom well into their childhood; long enough for Mario to meet Wario. It's understandable how some people might argue against that being canon, but seeing as how the TV show was made by DiC (correct me if I'm wrong on that) and the movie was made by Lightmotive and Allied Filmmakers, which are both third party companies, the comic seems to be the only Extended Universe thing that you CAN consider canon, since it was the only one actually made by Nintendo and was shown in Nintendo Power itself.
Anyway, to get back on topic: Mario and Luigi seem to have been born in the Mushroom Kingdom; that's a given. However, since Bowser, and what seems to be the beginnings of the Koopa Klan, were already aware of the brothers existence in SMW2, then it seems only logical that their family, and possibly the Mushroom Kingdom itself, would have feared for their safety. Thus, they might have transported them to Earth in an attempt to keep them safe until they reached maturity and could return home. Since Mario and Luigi are also always refered to as Italian and not American, it seems only logical that Mario and Luigi would hail from Italy itself. PLUS! If you take into account the fact that Donkey Kong '94 and Donkey Kong Land state that the original DK game took place not in Brooklyn, but in Big Ape City on DK Island, it's possible that Mario and Luigi have never been to America at all. Unless the other games like Wrecking Crew and such also state that they took place in Brooklyn, which I'm not aware of.
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"The bigger they are, the harder I fight."