And like one might expect, I still only really "get" art that has a close enough analog to the work I do. So... sculpture? Right out.
And like others have brought up, art is contextual. One fundamental fallacy I see people make is that all pieces of work need to be conceptually complete and self-contained. A lot of good art can only be appreciated in aggregate.
FWIW, I don't "get" any of the art in the article either, save for the photograph of the woman. It's important to know that for photography geeks, it's often not about the subject, but rather about geometry, tonality, color, and more abstract notions. After all, there's a huge genre of photography dedicated to the everyday and the banal, whose only real claim to anything is beauty in composition and light.
As with all art though, there are territories that are incredibly facile, and therefore tend to be heavy-handed. Pictures of kissing couples, that "ring in a book with the shadow of a heart" thing wedding people use all the time, portraits of the homeless, etc etc. Stuff that's conceptually and technically been done to death, and IMO makes the artist appear more self-absorbed than anything else. Likewise, my gut reaction to the "money against the vagina" shot is "how obvious and ham-fisted", but that's just me. It's a me-too "exploration" of a topic that's been explored to death, without adding anything new to the concept or discourse.
In general, if you want art that you might find personal connection in, look at artists without an ego the size of the moon, and run far, far away from ones that do.
Like Picasso, Dali, Caravaggio and Michelangelo?
Yes, but I think the major difference between this and most modern artists that you'll find in galleries and museums is that photographers are far more likely to admit that their work is nothing but beauty in composition and light, without piling on claims of symbolic meaning or attributing some abstract concept.
I'm mostly indifferent to the work of most modern installation artists; it's the self-importance of it all that I bristle at.