The plaque commonly displayed the name of the ship, as well as its class and shipyard of origin. Many later plaques also displayed the ship's official motto, plus a list of notable Starfleet officers involved in the assembly of the vessel.
After earlier being made to wait for quite some time by the Sheliak, Captain Picard took his time answering their hail, inspecting the ship's dedication plaque in 2366. (TNG: "The Ensigns of Command")
When USS Voyager found the USS Equinox in 2376, Captain Janeway noted that the Equinox's plaque had fallen, and advised that they should hang it back up. Similarly, after days of battling with the Equinox after they betrayed the Voyager crew, Voyager's dedication plaque fell down. Janeway noted that, after years of battles, it had never fallen down before, and in a symbolic gesture, they put it back "where it belonged." (VOY: "Equinox", "Equinox, Part II")
Thomas Jefferson, the 3rd US President, was quoted on the dedication plaque of the USS Yamato in "Where Silence Has Lease". The quote was: "I have sworn eternal hostility against every form of tyranny over the mind of man." (Star Trek Encyclopedia (1st ed., p. 380))
According to the Star Trek Encyclopedia (4th ed., vol. 2, p. 101), the dedication plaque on the Galaxy-class USS Odyssey, seen in the Star Trek: Deep Space Nine episode "The Jem'Hadar", had the following quote: "Its origin and purpose, still a total mystery." The quote is inspired by Dr. Floyd from Arthur C. Clarke's 2001: A Space Odyssey:
"Dr. Floyd: [prerecorded message speaking through TV on board Discovery while Bowman looks on] Good day, gentlemen. This is a prerecorded briefing made prior to your departure and which for security reasons of the highest importance has been known on board during the mission only by your H-A-L 9000 computer. Now that you are in Jupiter's space and the entire crew is revived it can be told to you. Eighteen months ago the first evidence of intelligent life off the Earth was discovered. It was buried forty feet below the lunar surface near the crater Tycho. Except for a single very powerful radio emission aimed at Jupiter, the four-million year old black monolith has remained completely inert. Its origin and purpose…still a total mystery."
The dedication plaque however, was not visible on screen in the final cut of the episode.
A dedication plaque was made for the bridge set of the USS Kelvin in Star Trek. However, due to camera angles and lighting conditions, it was illegible. The plaque was located adjacent to the turbolift. The Star Trek Encyclopedia (4th ed., vol. 1, p. 192) contains a graphic of this plaque, which includes the ship's name, registry number, commissioning stardate of 2225.5 at San Francisco, California, and the motto "All glory comes from daring to begin." The plaque does not include the ship's class.
In the non-canon Star Trek: Titan premier novel Taking Wing, Captain Riker has a tough time selecting a proper quote for the USS Titan's dedication plaque. It has never been implied, one way or the other, if it is standard procedure for a ship's captain to choose the quote on their own ship's plaque. In the next novel The Red King, he chooses the Vulcan maxim "Infinite Diversity in Infinite Combinations" (IDIC) in tribute to the Titan's crew, which following with the Luna-class's design, was one of the most diverse in Starfleet history with less than 15% of the crew being Human. One of Riker's other choices was a verse sung by Jazz legend Teresa Brewer: "It Don't Mean a Thing If It Ain't Got That Swing."
In the first issue of the IDW Publishing comic Star Trek: Spock: Reflections, Captain John Harriman had a memorial plaque dedicated to James T. Kirk installed on the USS Enterprise-B a year after it left spacedock for repairs in the section of the ship where Kirk was at the time believed to be killed. Although Harriman knew it wasn't regulation, he felt it was the right thing to do.