Flag
Flags and banners were decorative pieces containing symbols that were used to represent a government, group or individual. Typically these pieces were used to represent patriotism or ownership.
Flags could also communicate in place of language, as in semaphore. (TV: Under the Lake)
On Earth
National flags
The flag of the United Kingdom was the Union Flag. When at sea, the flag was the similar Union Jack. (TV: The Idiot's Lantern)
The flag of the United States of America, distinguished by its stars and stripes, was known as Old Glory. (COMIC: Backtime)
Other
Plain white flags were normally used in the event of a surrender. The Tenth Doctor, holding a sheet of A4 paper on a stick, met a group of Cybermen, jokingly apologising for not having an actual white flag. (TV: Doomsday)
Elsewhere
The Threllip Empire flag was grey. (AUDIO: Living Legend) The Tragellan Empire flag was red. (COMIC: Beneath the Skin) The Karturan Congruity used a holographic flag. (AUDIO: The Forever Trap) The Women's Institute had a flag with a crest. (PROSE: I Am a Dalek)