Occasionally I've run across references to a French artist who supposedly committed suicide because he was driven mad by the mystery of the Mona Lisa's smile. There aren't many details to the story. The Telegraph, in an article from 2003, summarizes the entire tale:
On June 23, 1852, a young French artist, Luc Maspero, threw himself from the fourth floor window of his Paris hotel. In a final letter, he wrote: "For years I have grappled desperately with [Mona Lisa's] smile. I prefer to die."
Many articles about the Mona Lisa casually include this tale without bothering to provide any references. For instance, it's mentioned in a 1999 Smithsonian article. Before that, the earliest reference I can find (searching in Google Books) occurs in an obscure 1966 work, Green Leaves: Harish S. Booch Memorial Volume. I came up empty-handed searching archives of nineteenth-century newspapers.
All versions of the tale, from 1966 onwards, are basically the same. No one ever supplies any information about who Luc Maspero was, or where the story of his unusual death originally came from. Tellingly, a 1961 article in the New York Times Magazine specifically about Mona Lisa's smile doesn't mention the Luc Maspero story. This suggests that the tale hadn't circulated very widely (at least in the English-speaking world) at that time.
Because the story of Luc Maspero sounds like an urban legend, and because I can't find any evidence to suggest that it's true, I'm going to list its status as "unlikely".