(covers information from several alternate timelines)
Betazed was a planet and the homeworld of the Betazoids, a warp-capable humanoid civilization. It was closely associated with the United Federation of Planets, but was never explicitly confirmed to be a member, yet multiple Betazoids were known to have served in Starfleet. The planet was run under the supervision of the Betazed government. (TNG: "Manhunt")
In 23rd century, con man Harry Mudd robbed a bank on Betazed. Using a time crystal, Mudd was able to learn everything about the bank's complex security measures, a fact he bragged about to Ash Tyler during their imprisonment in 2256. (DIS: "Magic to Make the Sanest Man Go Mad")
The Betazed Federation ambassador during the 2360s and '70s was Lwaxana Troi, daughter of the Fifth House, holder of the Sacred Chalice of Rixx, heir to the Holy Rings of Betazed. (TNG: "Angel One", "Manhunt"; DS9: "The Forsaken")
During the Dominion War in 2374, Betazed was invaded by the Dominion from the Kalandra sector. The Federation Tenth Fleet had been assigned to defend Betazed and its outlying colonies, but was caught out of position on a training exercise. The obsolete and undermanned planetary defense system was overwhelmed, and the planet fell in under ten hours. With Betazed captured, other nearby worlds, including Vulcan, Tellar, Alpha Centauri, and Andor, were at risk of Dominion attack. (DS9: "In the Pale Moonlight")
Near the end of 2374, the Second Fleet struck the Dominion forces occupying Betazed three times in a single month. However, each time the Dominion sent reinforcements and fortified their surface positions. (DS9: "The Sound of Her Voice")
Points of interest
- DIS: "Magic to Make the Sanest Man Go Mad" (mentioned only)
- TNG: "Ménage à Troi"
- TNG: "Dark Page" (mentioned only)
- DS9: "In the Pale Moonlight" (mentioned only)
- Star Trek Nemesis (mentioned only)
According to the script for "Q-Less", the pronunciation for Betazed was "BAY-tuh-zed". 
The scenes on Betazed in "Ménage à Troi" were originally written with studio filming in mind as their shooting locale, because the notion of using filming locations was at first prohibited for the episode. When more money became available, however, this plan was revised, with a day of location shooting planned instead. (Starburst, Special #29, p. 57) The footage was ultimately filmed at the Huntington Library Botanical Gardens in Pasadena, California, where "Justice" had also been filmed two and half years earlier. (Star Trek: The Next Generation Companion)
According to Star Trek: Star Charts (p. 33), Betazed was the fifth planet in the Betazed (Beta Zeta) system. The official name of the government was the Fifth House of Betazed, which governed this planet from the capital city of Rixx. Betazed was admitted into the United Federation of Planets in 2273. As reported in the census of 2370, the planet was populated with 1.3 billion Betazoids living there. Betazoids had been warp-capable since antiquity. Major attractions on this world included Lake Cataria, Janaran Falls, and the University of Betazed. The system was named by the 21st century Human John Burke, chief astronomer of the Royal Academy.
According to Star Trek: Star Charts (pp. 36 & 48) and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), the Betazed (Beta Zeta) system was located in the Alpha Quadrant. The primary was a G-class star. In October 2374, the Dominion won the Battle of Betazed and claimed the system. (Stellar Cartography: The Starfleet Reference Library ("Stellar Cartography" p. 41; "The Dominion War: Strategy and Battles, 2373-75") placed this event in September 2375.)
Alternately, The Worlds of the Federation places the Betazoid homeworld, called Cyndriel, as the fifth planet in the Beta Veldonna system. The Star Trek: The Next Generation First Year Sourcebook puts Betazed as the second planet in the Beta system, and Planets of the UFP describes Betazed as the second planet in the Betazed system, with its capital city being Medara. The Worlds sourcebook places Betazed as the third planet in its system.
The Star Trek: Federation Travel Guide describes local attractions including the University of Betazed (with classes open to visitors), Janaran Falls, and the ornate mansions of Betazed's "exalted houses" - especially the Fifth House. Restaurants include "The Oskoid" with its vegetarian menu and "Apolloni's Retreat" with its uttaberry pudding. The recommended lodging option is "The Mountain House" at Lake Cataria, allows visitors a view of beautiful sunsets and swimming during the appropriate season. A Betazoid key phrase is "May good fortune attend you."