It wouldn’t be the most, but the Cape Neddick Lighthouse in Maine is certainly among the most painted and photographed buildings in the nation.
For most painted and photographed in the world, I’ll guess (if you can count them as buildings) the Pyramids, strictly since they’ve been depicted for thousands of years and nobody goes to Egypt without photographing them.
Quite possibly. Then again, just because a building is around for a long time doesn’t mean that people are painting it.
One thing that might give Motif #1 a leg up is that the town of Rockport (or perhaps it’s Gloucester) sponsors a contest every May in which artists from around the country (or perhaps world) gather to paint it. The winner gets his or her work displayed in Gloucester City Hall for six months. Apparently thousands show up for the event. That alone gives the thing sheer numbers.
But I have to wonder how such a number can be counted. I painted it on Monday and it’s not like I registered my work with any global database. It’s not like I caused the “official” count to jump from 45,392 to 45,393.
It may well be an unfalsifiable claim.
Hey, I painted that two years ago! 
Golden Gate [Bridge] = 1,790,000
13,800,000 for “my house”. We have a winner here: it’s my house. (That must be why there are those hordes of photographers and painters that I nearly run over as I back out the driveway each morning :))
You wouldn’t have such a problem if you’d close those friggin’ drapes!
That’s the one that came to my mind immediately.
Damn you, I came in here to cite that!
shakes fist
I will nominate the Smithsonian. The pictures of all the stuff inside are also showing the structure of the building. I think it could make it on the exterior photos alone.
The building that the Times square sign is mounted on is runner in the race I’ll bet.
I’ll mention The Cinderella Castle in Walt Disney World Resort, and The Sleeping Beauty Castle in Disneyland. Walt Disney World Resort is the number one theme park in the country, and the Cinderella Castle has to be the most photographed building there.
Shows what you know. “My home” gets 22.2 million hits. Clearly the hordes you see outside are the ones that had to go somewhere else because they couldn’t fit at “my home.”
I only get 1,370,000 for “my house”, so my house must be less popular than your house. Nope - “your house” only gets 867,000.
Are you sure you are searching for images?
Most painted building? I nominate this.
I’d count the Statue of Liberty, becauase it has stairs and elevators inside, and you can go up into the top. it’s a cleverly disguised building.
As for buildings that are not trying to fool anyone, I’d think the White House or the Chrysler building are up there. At least for non-currency depictions, such as a poster mentioned above :D.
How about the British Parliament Building (containing Big Ben’s tower)? Or the Tower Bridge? (I’d count that as two buildings).
Um, well, no, because I don’t think those are in America.
IMHO, the query is unanswerable. I mean, how could you really count?
My Dad and I had a conversation recently, similar to this. It wasn’t restricted to the US, though. Some idears:
Thomas Jefferson Expansion Memorial Monument- aka The Arch
The Space Needle
New York Stock Exchange
And the many cool suggestions from above. The Flatiron Building and the Disney Castles we did NOT think of. And should have! 
Don’t know about the US, but I suspect that the most photographed building in the world is the Taj Mahal.
Forget the Taj Mahal, the most photographed (globally) is the Great Pyramid of Cheops.
…two coats!
For the world I would like to nominate the Vatican. I was going to say the Great Pyramid of Cheops as already stated, or the Sphinx in Giza. Buckingham Palace seems to get every tourist to take a picture. The temple Angkor Wat in Cambodia. You will recognize it, if you see it. Angkor Wat link.