|Owner:||United Federation of Planets|
In the course of his duties on the Hood, Will Riker refused to allow Captain DeSoto to transport to the surface of Altair III for an away mission. Riker felt the mission was too dangerous to expose the ship's CO to such a risk. (TNG: "Encounter at Farpoint", "The Pegasus")
Service from 2364-2369
In 2364, the Hood rendezvoused with the USS Enterprise-D in orbit of Deneb IV, to transfer crew and equipment, including the ship's new first officer, William Riker, CMO Beverly Crusher, and Geordi La Forge, as well as Admiral Leonard McCoy, who inspected the medical facilities of the Enterprise. (TNG: "Encounter at Farpoint")
Two years later, the Hood was dispatched to the Romulan Neutral Zone in order to counter a possible Romulan sneak attack emanating from a cloaked Romulan base on Nelvana III with the goal to retake the Neutral Zone. (TNG: "The Defector")
The Hood was also part of Captain Picard's task force in 2368 to blockade the Klingon-Romulan border in order to cut off the Duras family from Romulan supplies. It served as a focal point and anchor in the tachyon detection grid, as it was linked to twelve other starships during the grid's initial deployment. (TNG: "Redemption II")
Dominion War service
The Hood fought in several engagements during the Dominion War. In early 2374, it was part of the task force that participated in Operation Return, the attempt to retake Deep Space 9. (DS9: "Favor the Bold", "Sacrifice of Angels")
There has been some controversy regarding the registry number of the USS Hood. The ship was first seen on-screen in TNG: "Encounter at Farpoint" in effect shots created by ILM, using the original studio model built by them for Star Trek III: The Search for Spock. No registry number was visible in these shots, but on pictures available on-line  , the model was clearly labeled "USS Hood, NCC-2541". Had this registry number remained canon, it would have made the Hood a close contemporary sister ship of the USS Repulse NCC-2544, further establishing a Starfleet practice that when a ship is named for a historical counterpart they are sometimes paired in the same class with other contemporary historical counterparts. The historical HMS Hood and HMS Repulse were contemporary British battle cruisers who shared a similar fate in World War II. Other examples where this was practiced were the USS Enterprise (NCC-1701) and the USS Lexington (NCC-1709) as well as the USS Monitor (NCC-61826) and the USS Merrimac (NCC-61827).
Apparently the original labeling was forgotten about or ignored by the production staff, as another, much higher registry number, NCC-42296, was devised later and used consistently in various LCARS graphics, for example the starship mission status and the screen showing Star Fleet Battle Group Omega.
The Hood's appearance in "Tears of the Prophets" was confirmed by John Gross and Karen Sickles of Digital Muse in a 25 June 1998 post by DS9 Visual Effects Supervisor David Stipes on the newsgroup alt.tv.star-trek.ds9. He noted that during the labeling of the CGI model of the USS Hood, a typographical error was made, mistakenly giving it the registry of the "NCC-42768." 
According to the Star Trek Encyclopedia the USS Hood, like its Constitution-class predecessor, was named for British admiral Sir Horace Hood, who fought and died in the Battle of Jutland during World War I, though that reference was dropped in the last edition of the Encyclopedia. The Star Trek Fact Files, part 86 states that the Hood was named for 18th century British admiral Samuel Hood (incidentally a direct ancestor of Horace Hood) after whom the ill-fated World War II British battle cruiser HMS Hood (launched and christened by Horace Hood's widow) was also named.
In the TNG PC game A Final Unity, if the Enterprise was destroyed, a message plays where a Starfleet admiral says that the USS Hood had been dispatched to investigate.
The USS Hood was one of the playable Excelsior-class starships in skirmish mode in Star Trek: Legacy.