Flag of the Federation

The Flag of the United Federation of Planets was a patriotic banner that consisted of a blue background with a white seal of the Federation above the words "UNITED FEDERATION of PLANETS."

In 2285, Kruge noted that with the Genesis Device, his officers could be sitting happily on their homeworld, with the exception of the flag of the Federation soaring above instead of that of the Klingon Empire. 

Traditions
The Flag of the Federation was often draped over the photon torpedo caskets of fallen Starfleet officers. 

In the 23rd century, starships such as the USS Defiant (NCC-1764) sometimes displayed the flag in their briefing rooms. 

The flag was also present at Starfleet courts martial, such as the one for the Nova Squadron in 2368. 

It was also displayed in Deep Space 9's briefing room during various official ceremonies, such as Worf's court martial, and the induction ceremony when Bajor (almost) joined the Federation. 

In accordance with an old Earth tradition, the flag was flown at a baseball game on the holosuite on Deep Space 9 when the Niners and the Logicians played a game in 2375. They also played the Anthem of the United Federation of Planets, taking their hats off and facing the flag. 

Background information
The first "Flag of the Federation" in Star Trek was visible across Spock's coffin in. As it hadn't been designed yet, the flag was missing from the Enterprise's conference room throughout The Original Series. An alternate Federation flag with yellow, orange, green and teal colors was seen in at the Khitomer Conference. 

According to the Star Trek Sticker Book (Pg. 9), by Michael Okuda, "At one time, it was thought that the three bright stars in the starfield might represent Earth, Vulcan, and the Klingon Homeworld, since during early episodes of Star Trek: The Next Generation it was thought that the Klingons might have actually joined the Federation. When later episodes made it clear they had not, the three bright stars were left undefined."

As described in Star Trek: Action!, in Deep Space Nine "Tears of the Prophets", someone was looking at the photon torpedo prop and couldn't quite put their finger on what was missing. They then disappeared, and came back with the Flag of the Federation to drape over it.