Just for fun, this post and a following one present some of those famous paintings that come to my mind.
The artists featured here, in alphabetical order, are Gustave Caillebotte (1848-1894), Salvador Domingo Felipe Jacinto Dalí i Domènech, 1st Marquess of Dalí de Púbol, best known as Salvador Dalí (1904-1989), Edward Hopper (1882-1967), Gustav Klimt (1862-1918), and Edvard Munch (1863-1944).
Maybe it has to do with the daring vertical split at the middle. Or perhaps the mood depicted. Then again, it could be the slightly simplified details that provide a slightly poster-like impression for modern eyes. Let's just say it might be all three possibilities along with a few more intangibles.
My guess is that it was the melting watches and that this was a fairly early Surrealist work by Dalí that generated initial notoriety. The fact that it's part of the New York Museum of Modern Art's collection and usually is on view contributes to its fame. Regardless, when I think of Dalí paintings, this one often comes to mind.
I chalk this painting's fame to the scene being depicted with its contrasts and psychological overtones. It can make viewers wonder what might have been happening there besides the obvious.
All that gilt, the ornamental detailing, the general abstraction of the composition. But the keys are the in-contrast depictions of fragments of people and the subject action.
It happens that I dislike this painting. As best I can tell, its fame has to do with the popularity of Freudian psychology decades ago and linkages people can make between the two.