The funeral of Captain Spock, 2285, using the Flag of the Federation
Funerals were ceremonial actions associated with the body of a dead humanoid. Funerals often differed across cultures and could play an important role in religious beliefs.
Officers in Starfleet often decided to have a traditional Earth "burial at sea", changed for starships to a burial in space. The deceased was put in a photon torpedo casing, with the flag of the Federation (or in some cases, the flag of Starfleet Command) draped across it. A senior officer or someone close to the deceased usually said a eulogy, after which another officer blew a Boatswain's whistle as those gathered for the funeral stood at attention. The torpedo casket was then launched or beamed into open space. (Star Trek II: The Wrath of Khan; DS9: "Tears of the Prophets"; VOY: "Alliances", "One Small Step", "Ashes to Ashes"; ENT: "Similitude")
The funeral of Lt. John Kelly, 2376, using the Starfleet Command Flag
In 2376, the Starfleet practice of burial in space directly conflicted with the Kobali practice of salvaging corpses for reanimation as a means of procreation. The body of the late Ensign Lyndsay Ballard of the USS Voyager, who died and was buried in space in 2374, was reanimated to become Jhet'leya. (VOY: "Ashes to Ashes")
Civilians were known, according to their wishes, to receive a similar burial, except they were placed inside a different kind of container and beamed into space. (TNG: "The Schizoid Man")
In 2369 a private Ferengi funeral was held at Quark's after the death of Zek. (DS9: "The Nagus")
Gul Dukat told Constable Odo that he attended the funeral for Gul Darhe'el, held on Cardassia. Darhe'el was buried under one of the largest military monuments. (DS9: "Duet")
A wake was an old Irish tradition that involved people staying with a person's body until the funeral. (DS9: "The Ship", "The Sound of Her Voice")
In 2373, Kira Nerys buried Tekeny Ghemor next to her father on Bajor. Gul Dukat had wanted to take him back to Cardassia, but Benjamin Sisko informed him that "Legate Ghemor's funeral arrangements have already been taken care of." (DS9: "Ties of Blood and Water")
Another similar practice was the memorial. One was held for Morn on Deep Space 9 in 2374. (DS9: "Who Mourns for Morn?")