A narcotic is a natural or synthetic addictive drug, such as opium, that reduces pain, alters mood and/or behavior, and sometimes induces sleep or stupor.
During the mid-21st century various Earth militaries controlled their soldiers through their use of narcotics. (TNG: "Encounter at Farpoint")
In 2254 Vina described the Talosian's addiction to experiencing events in the thought record by comparing it to a narcotic. (TOS: "The Menagerie")
The inhabitants of the Federation colony Turkana IV often turned to narcotics as an escape from the great poverty and violence that existed there. Natasha Yar described her knowledge of the effects of narcotic drugs, from experiences she witnessed on her homeworld, to her fellow crewmates, Data and Wesley Crusher in 2364; they did not understand why anyone "would voluntarily become dependent upon a chemical." (TNG: "Symbiosis")
The Ornarans of planet Ornara suffered from an addiction to the narcotic created by the Brekkians known as felicium circa 2364. (TNG: "Symbiosis")
Ketracel-white, used by the Dominion to control Jem'Hadar soldiers in the 24th Century, shared many of the same pharmacological traits as a narcotic. (DS9: "The Abandoned", et. al.; "Star Trek: Insurrection")