The Museum of Modern Art (MoMA) is an art museum located in Midtown Manhattan in New York City, USA, on 53rd Street, between Fifth and Sixth Avenues. It has been singularly important in developing and collecting modernist art, and is often identified as the most influential museum of modern art in the world. The museum's collection offers an unparalleled overview of modern and contemporary art, including works of architecture and design, drawings, painting, sculpture, photography, prints, illustrated books and artist's books, film, and electronic media. MoMA's library and archives hold over 300,000 books, artist books, and periodicals, as well as individual files on more than 70,000 artists. The archives contain primary source material related to the history of modern and contemporary art. It also houses an award-winning fine dining restaurant, The Modern, run by Alsace-born chef Gabriel Kreuther.
http://www.moma.org/

The Musée du Louvre or officially the Grand Louvre — in English, the Louvre Museum or Great Louvre, or more simply the Louvre — is a historic monument in Paris and the national museum of France. It is a central landmark of the city, located on the Right Bank of the Seine in the 1st arrondissement (neighbourhood). It's the most visited museum in the world and arguably the most famous one. Nearly 35,000 objects from the 6th millennium BC to the 19th century AD are exhibited over an area of 60,600 square metres (652,300 square feet).
http://www.louvre.fr/llv/commun/home.jsp?bmLocale=en

The Metropolitan Museum of Art is an art museum located on the eastern edge of Central Park, along what is known as Museum Mile in New York City, USA. It has a permanent collection containing more than two million works of art, divided into nineteen curatorial departments. The main building, often referred to simply as "the Met," is one of the world's largest art galleries, and has a much smaller second location in Upper Manhattan, at "The Cloisters," which features medieval art.
http://www.metmuseum.org/

This is one of the coolest structures insides and out in NYC.
http://www.guggenheim.org/

The Museo del Prado is a museum and art gallery located in Madrid, the capital of Spain. It features one of the world's finest collections of European art, from the 12th century to the early 19th century, based on the former Spanish Royal Collection. Founded as a museum of paintings and sculpture, it also contains important collections of more than 5,000 drawings, 2,000 prints, 1,000 coins and medals, and almost 2,000 decorative objects and works of art. Sculpture is represented by more than 700 works and by a smaller number of sculptural fragments. It is one of the most visited sites in Madrid.
http://www.museodelprado.es/

The British Museum is a museum of human history and culture situated in London. Its collections, which number more than seven million objects, are amongst the largest and most comprehensive in the world and originate from all continents, illustrating and documenting the story of human culture from its beginning to the present.
http://www.britishmuseum.org/

The Museo Nacional de Antropología (MNA, or National Museum of Anthropology) is a national museum of Mexico. Located within Chapultepec Park in Mexico City, the museum contains significant archaeological and anthropological artifacts from the pre-Columbian heritage of Mexico, such as the Piedra del Sol (Aztec calendar stone) and the 16th-century Aztec statue of Xochipilli.
http://www.mna.inah.gob.mx/

The Tate Modern in London is Britain's national museum of international modern art and is, with Tate Britain, Tate Liverpool, Tate St Ives, and Tate Online, part of the group now known simply as Tate.
http://www.tate.org.uk/

This has always been my favorite museum in the world. Amazing tREX bones!
http://www.amnh.org/

The Uffizi Gallery (Italian: Galleria degli Uffizi, Italian pronunciation: [ˌɡalleˈriːa ˈdeʎʎi ufˈfiːtsi]), one of the oldest and most famous art museums in the world, is housed in the Palazzo degli Uffizi, a palazzo in Florence, Italy.
http://www.historiaweb.net/galleria_degli_uffizi/

The Vatican Museums (Italian: Musei Vaticani), in Viale Vaticano in Rome, inside the Vatican City, are among the greatest museums in the world, since they display works from the immense collection built up by the Roman Catholic Church throughout the centuries. Pope Julius II founded the museums in the 16th century. The Sistine Chapel and the Stanze della Segnatura decorated by Raphael are on the visitor route through the Vatican Museums.
http://en.wikipedia.org/wiki/Vatican_Museums

Mexico with 2 museums in this topic, great!

The New Museum of Contemporary Art, founded in 1977 by Marcia Tucker, is the only museum in New York City exclusively devoted to presenting contemporary art from around the world. Over the past five years, the New Museum has exhibited artists from Argentina, Brazil, Bulgaria, Cameroon, China, Chile, Colombia, Cuba, Germany, Poland, Spain, South Africa, Turkey, and the United Kingdom among many other countries. The Museum presents the work of under-recognized artists, and has mounted ambitious surveys of important figures such as Ana Mendieta, William Kentridge, David Wojnarowicz, Paul McCarthy and Andrea Zittel before they received widespread public recognition. In 2003, the New Museum formed an affiliation with Rhizome, a leading online platform for global new media art.
http://www.newmuseum.org/

The Museum of Design Zurich (German: Museum für Gestaltung Zürich) is a museum for design, visual communication, architecture and handicraft. It is located in Zurich's Kreis 5, close to Zürich Hauptbahnhof. In a building that once housed the School of Arts and Crafts the museum runs a large exhibition hall and the gallery, the foyer, the cafeteria and the shop as well as the vestibule to the lecture hall. The museum's other exhibition locations are the Museum Bellerive, which occupies a former villa on the shores of Lake Zurich, and the Plakatraum (poster room). The museum's four extensive collections (Poster Collection, Graphics Collection, Design Collection and Applied Art Collection) are of international importance and are open to the public on request.
http://www.museum-gestaltung.ch/collections/poster.html