The Guggenheim museums are art museums around the world owned by the Solomon R. Guggenheim Foundation, and they are as famous for the art they display as they are for their architecture:
The Guggenheim Museum, located in Manhattan, New York, was the first of the Guggenheim museums, opening in 1959. The Solomon R. Guggenheim Foundation commissioned Frank Lloyd Wright, who is most famous for his house,
Fallingwater. Wright did not like New York as an architectural location, as he found it too overdeveloped and overpopulated; "I can think of several more desirable places in the world to build his great museum, but we will have to try New York." (Wright, 1949). Indeed, Wright scoured the city for the ideal location. As an architect who deeply appreciated nature, Wright settled on the Upper East Side, across from New York's grassiest location, Central Park, although he did attempt to establish the museum in the park.
The museum design, inspired by the spirals of a nautilus shell, is a fitting example of contemporary and organic architecture, but Wright's innovations did not end on the outside. He also reformed the way museum-goers traverse through a museum. Visitors take an elevator up to the top, and work their way down through the exhibits along a large, spiral ramp. They are sure to see every piece in the museum, and never have to retrace their steps the moment they enter.
Completed six months after Wright's death (he was 91 years old!), the Guggenheim Museum is regarded as Wright's last significant work. Criticisms of the building include concerns that the form of the building detracts from the artwork it houses, and that artwork cannot be properly viewed on a curved wall.

Guggenheim Museum Bilbao lies on the
Nervion River waterfront in Bilbao, Spain. Through a design competition for Bilbao's first major cultural center, Frank
Gehry was chosen to be the architect. With the curves and curls, the structure is undeniably characteristic of
Gehry and his
deconstructivism style, which strives to portray buildings in constant states of unrest. Interestingly enough, he commented, "I used to be a symmetrical freak... I realized that those were chains, that Frank Lloyd Wright was chained... You don't need that if you can create spaces and forms and shapes." To keep the museum in touch with its Guggenheim sister in New York, though,
Gehry did incorporate a high, sky-lighted space akin to that of Wright's rotunda. His design also integrated the surroundings by letting the suspension bridge poise over a section of the museum, and by making the museum's profile that of a ship as it sits on the harbor. Furthermore, the side of the museum overlooking the water is sheathed in reflective titanium while the other half that greets the city is built with Spanish limestone.

Currently being developed in
Abu Dhabi of the United Arab Emirate is another
Gehry Guggenheim. (You can barely tell, though, can you?) The museum will be the largest in the Guggenheim collection and the largest installment of the
UAE's cultural revitalization. The museum aims to be completed by 2011.
These are the only Guggenheim
s that stand out architecturally. The Guggenheim foundation even seems to think so, offering the option to "Browse by Architecture" only for Guggenheim New York and Bilbao.
Abu Dhabi's will surely be on the list, too, once it finishes construction.
Not to be exclusive however, I've listed the less ostentatious
Guggenheims as well:

The Guggenheim museum in Venice, Italy is named after Peggy Guggenheim, niece of Solomon R. Guggenheim, and an avid art lover. She was also born into a very rich family. With her money, she bought a large collection of art and made many attempts at establishing a museum. Eventually, she purchased the
Palazzo Venier dei Leoni on the Grand Canal in Venice. Though the purchase was, at first, for
residential purposes, she later donated the palace to the Guggenheim Foundation, along with her art.
The palace, built by Lorenzo
Boschetti, dates back to the mid 18
th century, and is unfinished. The floor plans, which are kept in the
Museo Correr in Venice, suggest that only a third of the palace was constructed. Reasons for the
incomplete building were probably financial, although another explanation is that the family across the canal, for fear of the palace being grander than their own, halted the construction. As an additional fun fact, what look like two tall hedges at the entrance of the palace are actually two columns covered in ivy.
Despite being only a partial palace, the museum's classical architecture and uniquely Venetian venue serve well as a Guggenheim art museum.
Finally, there is
Deutsche Guggenheim in Berlin, Germany. Named after the
Deutsche Bank, which helped establish the museum and resides on the floors above. It is a sandstone building dating from the 1920's and the interior gallery was designed by architect Richard
Gluckman.
Other future
Guggenheims include the twenty-four story Guggenheim Guadalajara in Mexico, and the Vilnius Guggenheim Hermitage Museum in Lithuania's capital. Guggenheim Guadalajara faces difficulties in construction so a completion date is unknown, and final designs for the Hermitage Museum, which is planned for the more distant future, have not yet been decided.