Mine is probably the Temple of Heaven, in Beijing.
Strictly because of its emotional resonance (for me, anyway), I nominate Cinderella Castle at Walt Disney World.
Neuschwanstein Castle
I visited there last year…
Westminster Abbey. I feel like it’s the genesis point of the English-speaking world.
The Ponderosa. Ok, Ok, I’ll stop.
If we’re talking real live buildings that people use and stuff, I’d say the Standard Oil Building in Chicago, the Rookery (Chicago), or the Wrigley Building (Chicago), or Union Station (Chicago). I like 'em all equally so I can’t pick one.
What an excellent question! My choice is the Secretariat Building of the United Nations. It’s distinctive against the NY skyline, and since my father used to work there I’ve been in it a lot. The Chrysler building is pretty good also.
Jeez, just one? I can’t!
We see it so often on TV that I think we forget what a good-looking building the White House is: File:WhiteHouseSouthFacade.JPG - Wikipedia
Frank Lloyd Wright’s Fallingwater is a masterpiece; I love it!: File:Wrightfallingwater.jpg - Wikipedia
Other than the obvious NYC skyscrapers, I’ve always liked the Johnson/Burgee-designed Bank of America Center in Houston: File:Bank of America Center Houston.JPG - Wikipedia
The Governor’s Palace in Williamsburg is a handsome building: File:Colonial Williamsburg Governor's Palace Main Building.JPG - Wikipedia
San Francisco has the most. impressive. city hall. evah!: File:Sfcityhall.jpeg - Wikipedia
Just one? I don’t think so, Tim.
Winchester Mystery House in San Jose, CA:
House on the Rock in Spring Green, WI:
For the Lily Pads, the Johnson Wax HQ in Racine, WI:
Full-on visual appeal: Sydney Opera House
And when it’s completed, probably Burj Dubai @ over half a mile tall:
The Palacio de Comunicaciones in Madrid is a nice looking structure.
The Temple of Heaven and Westminster Abbey have already been mentioned. I somehow made it to Beijing without seeing the ToH, so another trip may be in order. I also didn’t see much of Westminster Abbey while in London, so I guess I’ll go back there as well.
Well hell, if we’re allowed more than one:
The Illinois State Capitol is pretty cool, in an imposing, gothic sort of way.
Also in Springfield, the Frank Lloyd Wright-designed Dana-Thomas House.
And my favorite place to spend a summer afternoon, Wrigley Field.
Picking just one, I’ll go with Casa Batlló.
I’m partial to the Gherkin in London.
I knew the architect, Jørn Utzon, had a falling out over this project. They reconciled in the ensuing years, and he designed some renovations and changes, but I just found out that he died a few months ago, having never seen the completed building. That almost breaks my heart.
I’m having to give this a lot of though for my own choice. Someday before I die, I want to see the Hagia Sophia. Until I do, I’m trying to think of a favorite among the buildings I have been to. There have been some great ones.
Darn it, I’m adding Arlington Park Racetrack (Arlington Heights)! 
Love it - and have a friend who works there!
I work in the Darth Vader Building which I think is kinda neat. It isn’t all that great from an outside view but Salvador Dali’s house is pretty dang cool.
I am partial to the Gulf Tower and Koppers Building, both in downtown Pittsburgh.
Here they are during the day (Koppers is on the left): http://www.skyscraperpicture.com/pittsburgh24.jpg
At night (From a different angle, the Gulf Tower is the taller): http://www.pbase.com/deadwing/image/78980555.jpg
I love the Cathedral of Learning at the University of Pittsburgh. My mom’s from Pittsburgh, and when I was a little girl she took me there and showed me the nationality rooms - but it was black, then! I didn’t know it was supposed to be yellow! I hadn’t been to many big universities with cool buildings then and I just thought that place was It - it’s very… reverent, you know? Somebody wanted to build a university building and called it a Cathedral of Learning - I dunno, I just love it. When you go there when classes are in session, it’s very much alive, full of students. Very cool.
Along similar lines, the Bodleian Library at Oxford moved me very personally.
I love all the beautiful Gothic cathedrals of the Old World, but my favorite is Winchester, because it’s the first one I ever saw. I was with a class of high school kids, and we all went in chattering and making idiots of ourselves, and when we got through the doors every single teenager shut up. 
I will always go to the National Cathedral in Washington DC if I get a chance. I spent a lot of time there as a kid and I know some of the nooks and crannies, but I feel like there’s still lots to discover, esp. since it wasn’t even finished until about 10 yrs. ago. I’m sure the ancient gothic cathedrals in Europe are way cooler, but this is the one I know.
I went to William and Mary and I really like the Wren Building. I liked to go to its “Great Hall” (not all that big) when empty and curl up into one of its round windows. A really nice peaceful hush there. I also had a few minutes on its back porch that changed my life forever