Slavery is the act of one sentient being controlling another in violation of the other's will. The one so controlled is referred to as a slave.
The Slaver Empire controlled a large galactic empire a billion years ago. The Slavers were known as the masters of all intelligent beings in most of the galaxy until one species revolted. (TAS: "The Slaver Weapon")
Slavery was common in ancient Earth, being practiced as late as the middle of the 19th century in the southern United States before being outlawed as a consequence of the American Civil War. These events had a great impact on human histroy, and were widely remembered to the point that, almost three hundred years later, when Charles Tucker III wondered aloud what kind of people the Orion slave traders the Enterprise had enountered were, Arik Soong caustically responded that, given the Florida native's southern accent, he likely had ancestors quite similar to them. (ENT: "Borderland")
Around this time, a Skagaran ship was sent to Earth. The vessel's crew abducted several thousand Humans that were taken to help the Skagarans start a colony, and serve as slave workers. (ENT: "North Star")
In 1937, the Briori kidnapped 300 Humans from Earth and took them back to an unnamed Class L planet in the Delta Quadrant and used them as slaves. The slaves managed to revolt and overthrow the Briori. (VOY: "The 37's")
The Romulan Star Empire used the Remans as a slave class from at least as early as the 22nd century until at least as late as 2379. (ENT: "United", "The Aenar"; Star Trek Nemesis)
In 2153, a humanoid named Zjod traded in sex slaves of various species from a shop in a floating bazaar on the Xanthan homeworld. (ENT: "Rajiin")
Slavery was also in operation in the mirror universe. The Tholians employed slave workers to gut the USS Defiant when it went through an interspacial rift and arrived in the mirror universe. They also employed alien slave masters, one of which was the Gorn named Slar. (ENT: "In a Mirror, Darkly, Part II")
The Orions used slave labor as late as the 23rd century. Common belief was that Orion women were slaves to the men, when it was in fact the opposite. In the 22nd century, Orions frequently kidnapped members of other species for slave trade. (ENT: "Borderland", "Bound")
During the Occupation of Bajor from 2328 to 2369 enforced labor was practiced at labor camps. This is a situation similar to slavery. (DS9: "Emissary")
The Kazon were a subjugated race, used as slave labor by the Trabe who had conquered their homeworld. They remained in captivity until in 2346, when Jal Sankur convinced the various Kazon sects to put aside their differences and rise up against the Trabe. In doing so the Kazon took the Trabe's ships and technology and forcing them to become a nomadic species, never allowing them to settle on a new world. (VOY: "Initiations", "Alliances")
When Bruce Maddox wanted to disassemble Data in 2365 in order to learn how to create more androids, Jean-Luc Picard considered Data's rights but failed to see the bigger picture. Guinan helped him realize that creating an entire "race" of Datas for use as tools would, in fact, be slavery. (TNG: "The Measure Of A Man")
In 2366, two Breen warships attacked the Ravinok, a Cardassian prison transport carrying 32 Bajoran prisoners crewed by 18 Cardassians. They forced that ship to crashland on the planet Dozaria. The Breen then used the survivors of this crash as laborers at a nearby dilithium mine. They remained slaves until freed by Major Kira Nerys and Legate Dukat in 2372. (DS9: "Indiscretion")
In the mid-2370s, the United Federation of Planets began using sentient holoprograms, the various types of outdated Emergency Medical Holograms, for slave labor purposes, utilizing them for difficult and dangerous tasks such as warp conduit maintenance and dilithium mining. The publication of the holonovel Photons Be Free by The Doctor, however, caused many in the Federation to begin changing their minds about this practice. (VOY: "Life Line", "Author, Author")