A flagship is a term referring to the status conferred upon a starship. Typically, a flagship is a vessel commanded by a flag officer (an admiral or similar rank). The term also properly applies to the ship of whatever commanding officer is in charge of a grouping of ships. A third, more colloquial usage of the term can mean that the ship in question is considered an "exemplar" of the best capabilities and virtues of the force it represents.
Federation-Starfleet
The USS Enterprise-D "flagship of the Federation."
The USS Enterprise served as the "flagship of the Federation" and of Starfleet, from 2364 to 2370. (TNG: "The Icarus Factor", "Sarek", "The High Ground", "Remember Me", "Ensign Ro", and more, "Force of Nature", "Parallels"; Star Trek Generations; DS9: "Bar Association")
While commanding the USS Sutherland, Data made continuous reports to the Enterprise-D, the flagship of the armada that employed the tachyon detection grid along the Klingon-Romulan border in 2368. (TNG: "Redemption II")
During the Borg threat of 2370, the USS Gorkon served as Vice Admiral Nechayev's flagship. (TNG: "Descent")
In 2373, Admiral Hayes led the Federation fleet against a Borg cube at the Battle of Sector 001 aboard his flagship. Following its destruction, Jean-Luc Picard, captain of the USS Enterprise took command of the fleet in order to coordinate the destruction of the Cube. (Star Trek: First Contact)
The USS Defiant frequently served as a flagship during the Dominion War. (Star Trek: Deep Space Nine)
In an unknown, alternate future timeframe, Admiral William T. Riker commanded the Enterprise-D as his flagship explaining that "they tried to decommission her about five years ago. One of the advantages of being an Admiral is you choose your own ship." (TNG: "All Good Things...")
First Federation
In 2266, the USS Enterprise encountered the First Federation flagship Fesarius, under the command of Commander Balok. (TOS: "The Corbomite Maneuver")
Klingon-Cardassian Alliance
Regent Worf commanded the Klingon flagship responsible for leading the assault, on several occasions, against Terok Nor and the Terran Rebellion. (DS9: "Shattered Mirror", "The Emperor's New Cloak")
- This vessel was only referred to as the "Klingon flagship" in the script, and was not identified as such in dialog.
Klingon Empire
At one time during Romulan Commander Toreth's illustrious career, she commanded a ship that attacked Klingon outpost was supposedly undefended, but was discovered to in fact be defended by attack force of cloaked warships, that took her squadron completely by surprise. Half of her ships were destroyed before the Romulans even opened fire, but when they did, the Klingon ships were no match for the Romulans. In fact, Toreth even destroyed the Klingon flagship herself, following the assault, she received the Sotarek Citation for her actions that day. (TNG: "Face of the Enemy")
For five years of Martok's civilian career, he served as a laborer aboard ShiVang's flagship. As he explained it, "then, as fortune would have it, the Romulans made a foolhardy attempt to board our ship. I earned a battlefield commission." (DS9: "Once More Unto the Breach")
IKS Negh'Var, "the new Klingon flagship."
In 2372, the Klingon Empire introduced the IKS Negh'Var as its new flagship. (DS9: "The Way of the Warrior")
When General Martok was later promoted to Supreme Commander of the Ninth Fleet, following the recapture of Deep Space 9 in 2374, Captain Benjamin Sisko offered to arrange the General quarters for him onboard the station. Martok declined, stating that "I'll keep my flag aboard the Rotarran. It's cramped but at least I'll feel like I'm still at war." (DS9: "You Are Cordially Invited") The following year, Romulan Senator Cretak complained the low priority given to repairing Romulan ships, and that "the Dividices and the Genorex have waited three weeks while a dozen Klingon ships have been given priority." Miles O'Brien explained to the Senator that although he planned the repair based on which ships had "the greatest need", which so-happened to be the Klingon ships. Major Kira Nerys interrupted, and in the interest of diplomacy, agreed to allow the two ships in for repair, but to do so was required to delay repairs to the USS Hornet and the Rotarran, adding "someone will have to tell General Martok why his flagship was bumped." (DS9: "Inter Arma Enim Silent Leges")
Romulan Empire
The Praetor's flagship, "the finest and proudest."
In 2266, the Praetor's flagship, "the finest and proudest," in the Romulan Empire attacked several Earth Outpost Stations. It was successfully beaten by the USS Enterprise, under the command of Captain James T. Kirk, and eventually destroyed by the ship's own commander in defeat. (TOS: "Balance of Terror")
The USS Enterprise encountered and was initially captured by three Romulan D7 class battle cruisers after illegally crossing the Romulan Neutral Zone in 2268. After a series of deceptions on the part of Kirk and Spock, aboard the Romulan flagship, they were successful in stealing its cloaking device. (TOS: "The Enterprise Incident")
In 2370, Romulan and Federation task forces built up along the Romulan Neutral Zone in response to anomalous readings in the Devron system, located within the Zone. Four Warbirds held position along the Romulan side of the Neutral Zone, led by the flagship Terix, commanded by Tomalak. (TNG: "All Good Things...")
In 2375, during the Battle of Cardassia, Admiral William Ross reported to Captain Sisko that "the Romulan flagship's been destroyed. Their entire line is collapsing." (DS9: "What You Leave Behind")
Terran Empire
In the mirror universe, in 2155, the ISS Enterprise served as the flagship of the Terran Empire. (ENT: "In a Mirror, Darkly") Later, Jonathan Archer declared the USS Defiant his flagship after he captured it and worked to quell the alien rebellion. (ENT: "In a Mirror, Darkly, Part II")