Worldwide, wealthy people have enjoyed showing off their wealth and power by building unusual buildings. Because nothing says "Look how rich and crazy I am" like building a huge mansion.
Location: Virginia, United States
Architect: Thomas Jefferson
Jefferson's Monticello is a large mansion build around Jefferson's love of dinner parties. To engineer the appearance of food magically appearing (and to hide the unfortunate truth behind the food's preparation), Monticello is made with rotating shelves to make food seem to magically pop from the walls. Wine chutes make full bottles of wine shoot into the room, and make empty bottles vanish.
Jefferson went deeply into debt from his parties, but kept his estate due to his prestige. He was a national founder, and collecting from him while he was alive just seemed massively tasteless to everyone involved. Of course, after his death, the collectors swarmed. Monticello is now a museum, run by someone other than Jefferson's family.
Name: Palace of Versailles
Location: Versailles, France
Architect: Louis Le Vau
His majesty Louis XIV wanted to send a message to the world. Namely: "I'm richer and smarter and have better taste than you do, nyah nyah." So he hired Mr. Le Vau to design a place where he and his entourage would enjoy a luxurious life of comfort with no concerns at all. It includes pumping large amounts of a nearby river to supply the numerous fountains and gardens with water, using the river's own flow to power the pump. Entire acres are dedicated to various arts, including painting, gardening, fountains, sculpture, and so on.
Unfortunately, the kind of attitude displayed proved disastrous for the French monarchy a few generations later. The Palace is maintained today as a museum.
Location: Berlin, Germany
Architect: Albert Speer
This thing was never actually built. Speer planned for it to be the capital of a German empire that covered Europe. It was to be built as a congressional building, in the same classical Greek style as the US's congressional building, but ludicrously larger. He planned it to be 315 meters long, 315 meters tall, and 74 meters tall.
Architects that examined his plans later claimed that while it could be built, it would suffer internal weather from condensing breath from the intended population inside, that the acoustics would either totally mute anyone speaking, or magnify their voice to deafening volume (experts disagree as to which), and that it would likely sink into Berlin's swampy soil from the immense weight.
World war 2 interfered with plans to construct this, obviously.
Name: Twin Towers 2
Location: New York, United States
Architect: Kenneth Gardner
New York's world trade center was destroyed in the 9/11 attacks. This is a proposed project to rebuild the building, taller, slightly wider, and with much larger windows. There are other projects, but this one is notable as being the most similar to the old structure.
Public opinion is that something should be built on the site, but disagreements rage was to exactly what and how to pay for it.
Name: Mile high tower
Location: Jeddah, Saudi Arabia
Architect: Pickard Chilton
This would be a skyscraper a full US mile (5280 feet) tall. But then they had to shorten it a bit, because the local soil couldn't support that much weight. Then they scrapped it altogether, because of the recent economic crisis. (Construction companies do reasonably expect to be paid to do work.)
Name: Burj Dubai
Location: Dubai, United Arab Emerates
Architect: Skidmore, Owings and Merrill (architectural company, presumably collectively)
"Burj" is Arabic for "Tower," so essentially the name means "Dubai Tower." This building was constructed partially to provide more business room and apartments, but mostly to show off the economic power of Dubai. It is now the tallest standing building in the world. Half as tall as the previous proposed entry, it has been finished in a hard time for Dubai, as all the foreign money is drying up in the recession. It was completed in October of this year.
Name: Forbidden City
Location: Beijing, China
Architect: Unnamed architect in the employ of the Ming emperor of China
When the Ming dynasty siezed power from the Song, (the kind of event that happened on a regular basis in China), the new emperor wanted to show off his newfound power, since he controlled more land after the rebellion. (Other powers were subsumed in the war, and assimilated into China). So he ordered a magnificent capital built, using his best architects, craftspeople, and with materials across his entire new empire. It was meant to glorify both the nation and himself, and included a temple to demonstrate piety.
The construction was immensely difficult, and the names of those involved has been lost, or more likely, never recorded in the first place. Sometime later, a lightning storm damaged the complex. Traditional Chinese belief about government is that a just emperor enjoys the "Mandate of Heaven," a contract that allows him absolute authority so long as he is just and fair before his people. Failure of the emperor to be just and fair would lead to the loss of his authority, which would transfer to something else. Successful rebellions indicated a transfer of the mandate, while unsuccessful rebellions indicated a strong warning that the emperor should change his behavior for the better. This lightning storm was seen as another kind of warning, that heaven and his people were angry at him for his extravagance.
Presumably he did solve this problem, as the Ming dynasty lasted for another 200 years.
The modern Chinese government does not use it as a government complex anymore, but maintains it as a museum of Chinese history.
As I said before, the world's greatest architecture was made mostly to brag about wealth and power, but are quite satisfying to tour.