I actually tend to avoid the most crowded attractions. Been to Paris several times, but never been to the Eiffel Tower or the Louvre (but the Arc de Triomphe and the Montmartre are cool places to visit).
That said, if I'm having to choose, I'm probably going to the Musee d'Orsay rather than the Louvre.
The fact is, as an artist, it's hard not to look at paintings by Picasso or Van Gogh and think, "Wow, they had such a big impact on me. I wanted to be like that."
That's part of the magic of the artist's brush — that it can so easily and effortlessly paint such a dramatic scene that you, the viewer, think you can be the same person as the artist.
As an artist, I'm very aware of how big the influence of an artist is. And as an individual, I'm extremely aware of how much an artist can influence me. That's why I'm very interested in people who can have the biggest impact on other people through their art.
Now, knowing it's famous, one can appreciate some of the justification for it. But it still wouldn't make at least my list of favorite paintings.