In the 22nd century, both the Earth Cargo Service and the Earth Starfleet made use of plasma cannons on their starships and shuttlepods. The civilian Y-class and J-class freighters each sported a single cannon and two turrets respectively, while Starfleet's NX-class prototype Enterprise (NX-01) sported several cannons before being fitted with the newer phase cannons in the year 2151, and its embarked OTV type K42 shuttlepod number 1 also sported dual cannons. (ENT episodes: "Fortunate Son", "Silent Enemy", "Horizon", "Awakening")
Alternate realities and timelines
In the mirror universe, these weapons were still used by the Terran Empire aboard their NX-class warships in 2155, although they also had phase cannons available. The ISS Avenger fired a spread of plasma cannon fire at the USS Defiant. (ENT episode: "In a Mirror, Darkly")
Temporal Cold War
In the 20th century of an alternate timeline created by the time-traveling faction of Na'kuhl led by Vosk, Nazi Germany used plasma cannons both as ground-based artilery and fitted to their Stuka dive bombers in 1944. (ENT episode: "Storm Front")
The Cardassian design of this weapon was designed specifically for planetary assault and thus was incapable of being used against starships. The plasma cannon was slung underneath the ship, where it launched a super-dense projectile at a planet's surface. Once the planet was struck, a significant amount of people were killed by the weapon's blast. (TNG video game: Armada II)
- Presumably, starships were capable of avoiding this version of the weapon which was why it was not used against starships.