A big reason for the popularity of the "Mona Lisa" is the fact that it was stolen from the Louvre in 1911. The image of the painting was placed on newspapers all over the world during the search for it, making it the most recognizable painting in the world.
Italian handyman Vincenzo Peruggia stole the "Mona Lisa" in 1911, and he wasn't caught until December of 1913. This gave the painting about two years to become the most famous painting in the world, even in its absence. The "Mona Lisa" was returned its permanent place in the Louvre in Paris. The museum attracted nearly 10 million visitors in 2012.