A "remake'" is a term used to described something that has been done again, sometimes with better quality, and usually with more features.
With some exceptions, remakes make significant character, plot, and theme changes. For example, the 1968 film The Thomas Crown Affair is centered on a bank robbery, while its 1999 remake involves the theft of a valuable piece of artwork. Similarly, when the 1969 film The Italian Job was remade in 2003, few aspects were carried over. Another notable example is the 1932 film Scarface which was remade in 1983 starring Al Pacino; whereas the 1932 is centered around bootleg alcohol, the 1983 version is based around cocaine. Sometimes a remake is made by the same director, for example the black and white A Story of Floating Weeds was remade into the color Floating Weeds by Yasujiro Ozu or the Dutch-language Spoorloos was remade into the English-language The Vanishing by George Sluizer.
Not all remakes use the same title as the previously released version; 1983's Never Say Never Again, for instance, is a remake of the 1965 film Thunderball; the 1966 film Walk Don't Run is a remake of the World War II comedy The More the Merrier. This is particularly true for films that are remade from films produced in another language, such as: Point of No Return (from the French Nikita), Vanilla Sky (from the Spanish Abre los ojos), and A Fistful of Dollars (from the Japanese Yojimbo).
In the recent history of cinema, remakes have generally been considered inferior to earlier versions by film critics and cinema-goers alike, e.g., The Birdcage, To Be or Not to Be. See the list of film remakes for exceptions to the generalization.
Another noteworthy (and increasingly common) development is the use of a successful (usually older) television series to be remade as a feature film. Like other film remakes, these often fare badly at the box-office and/or are considered a poor reflection on the source material (e.g. The Beverly Hillbillies, Bewitched, My Favorite Martian, Dudley Do-Right); however, some have gone on to become successful film franchises (e.g. Scooby-Doo, The Addams Family, Mission: Impossible).
There are video game remakes as well. Some are more complete remakes where much of the game was changed such as Metroid: Zero Mission being a remake of the original Metroid. Some of them are simply the original game with some added content, such as the Xbox 360 and Wii versions of Bully. There are even some that are a mixture of the 2, where there is a good mix of old and new content, such as the Final Fantasy remakes for the DS and Super Mario 64 DS
One area where television remakes are particularly common is trans-Atlantic ports, where US shows are remade for the UK (see List of U.S. television series remade for the British market) or more frequently, UK shows are remade for a US market (see List of British television series remade for the U.S. market). An interesting example is Three's Company, a US remake of the British Man About The House: not only was the original show re-created (with very few character or situation changes made, at least initially), but both series had spin-offs based on the Ropers (in the UK, George And Mildred, in the US, The Ropers), and both series were eventually re-tooled into series based on the male lead (in the UK, Robin's Nest, in the US, Three's A Crowd).
While television remakes of theatrical films have occurred (e.g. The Odd Couple, F/X: The Series), far more common are TV series that are (more or less) direct spin-offs of successful films (e.g. Highlander: The Series,The Young Indiana Jones Chronicles, Stargate SG-1, Terminator: The Sarah Connor Chronicles).