A phaser cannon was a type of directed energy cannon weapon, a powerful phaser bank, used by at least the United Federation of Planets and Species 6339. It has been utilized as a ground vehicle mounted turret gun and an embedded starship-mounted weapon system. (DS9: "The Search, Part I", "Shattered Mirror"; VOY: "Infinite Regress"; Star Trek Nemesis)
Ship-mounted phaser cannon
The ship-mounted Federation cannon is an optronically targeted phaser. (VOY: "Live Fast and Prosper") It was presumably first introduced in the Defiant-class starship. In the mirror universe, the Defiant phaser cannons were called multi-targeting phaser banks by the Klingons. (DS9: "The Search, Part I", "Shattered Mirror")
The four cannons of the Defiant-class were usually seen firing phaser bolts simultaneously in short rapid-fire bursts and in only one direction. The cannons could also fire beams. (DS9: "Destiny") The combined firepower of the four phaser cannons of the Defiant appears to have beeen almost as powerful as the combined firepower of two wing-mounted disruptor cannons on a Klingon Bird-of-Prey. (DS9: "Favor the Bold")
On the Defiant-class the plasma conduit was run through the primary phaser coupling to almost double the power of the phaser cannons. On most Federation ships this would have significantly reduced the warp drive efficiency. (DS9: "Defiant") Phaser safeties were engaged before the weapons array was brought on-line and the phaser cannons charged to full power. (DS9: "The Changing Face of Evil") When the cannons were charged, fifteen-percent plasma was bled to the phaser matrix. (DS9: "For the Uniform") There was also a separate phaser generator from the emitters. (DS9: "Starship Down") There were also phaser reserves that could be emptied, for example to strengthen structural integrity. (DS9: "The Sound of Her Voice") There was a thirty-inch long power cell in the phaser array on the Defiant-class starships that was easily used up and needed to be replaced. (DS9: "Favor the Bold")
With extensive modifications, involving shunting the primary phaser relay through the warp drive, and bypassing the plasma emitter from the emitter coupling servos to avert an overload, phaser cannon array could be modified to emit a phaser beam wide enough to encompass an entire comet and vaporize it evenly from a distance of ten kilometers. (DS9: "Destiny")
In 2373 the throughput reading of the phaser relay on the Defiant was 148.7. Lieutenant Commander Worf and Ensign Nog attempted to increase the relay efficiency. This process involved recalibrating the emitter stage after the interface program was initialized and prefire chamber charged. (DS9: "Soldiers of the Empire")
Other species phaser cannons
Species 6339 utilized phaser cannon technology. One of their vessels, commanded by Ven, encountered by the USS Voyager in 2375, was found to possess 22 phaser cannons on the aft section alone. (VOY: "Infinite Regress")
Ground vehicle-mounted phaser cannon
Ground vehicles could be equipped with a personnel-operated phaser cannon. The Argo shuttlecraft, attached to the USS Enterprise-E, was equipped with a buggy which was armed with such a device. (Star Trek Nemesis)
- Optronic weapons array
- Phaser pulse
- Photon pulse
- Proximity blast
- Pulse cannon
- Tetryon pulse launcher
It is a common interpretation that the Federation phaser cannon was also developed specifically against Borg ships, as the Defiant-class was designed only for the one purpose, to fight and defeat the Borg and it was presumably the first shiptype to use a phaser cannon. (DS9: "The Search, Part I")
The script of DS9: "Destiny" named the weapon a Gatling gun phaser. There is however no evidence of any rotating barrels. On-screen, in the dialogue, the Defiant cannons were called simply phaser banks (DS9: "Second Skin", "The Adversary", "For the Uniform", "Favor the Bold", etc.) or just the phaser array. (DS9: "Defiant", "Destiny") The four cannon simultaneous phaser volley of fifteen shots (sixty bolts total) was called "a standard burst" in "Destiny". Star Trek: Starship Spotter identifies the classification of the cannons as Type XII phasers.
In the first draft of the script of Star Trek: First Contact  the USS Enterprise-E was also intended to have port and starboard batteries of rapid-fire phasers resembling Gatling guns in their effect. They were able to destroy a Borg cube before the Borg ships adapted their shields to the cannons.
In the Star Trek: Deep Space Nine Technical Manual, the Defiant's phaser cannons are called "pulse phasers" or "pulse phaser cannons." The weapon combines several new technologies, such as nearly flawless emitter crystals, rapid discharge EPS capacitance banks and high-speed beam-focusing coils. The pulses are structured like a layered onion. As a result, the target contact is more difficult to disperse than a standard phaser beam. On the Defiant, the EPS weapon-power conduits have been truncated to provide a near zero lagtime between activation command and beam launch. (pg. 123, 132, 133) Miranda-class starships were also armed with two pulse phaser cannons. (pg. 154)
In the script of Star Trek, when Captain Christopher Pike is recruiting James T. Kirk to join Starfleet, he comments on the cadets who fought with Kirk in the Shipyard Bar, that "they'll run home to momma the minute they're looking down the barrel of a Klingon phaser cannon." This suggests Klingons were using phaser cannons during the mid-23rd century of the alternate reality. 
According to the Pocket Books novelization The Search, by Diane Carey, the phaser cannon is called a triple-redundant interlocking phaser array. According to the novel A Sea of Troubles, the Miranda-class starship USS Samson (USS Samson (Miranda class) at Memory Beta, the wiki for licensed Star Trek works) was upgraded with Defiant-class type pulse phasers. According to the novel Gods of Night, the Vesta-class (Vesta class at Memory Beta, the wiki for licensed Star Trek works) starships were armed with Mark XII phaser cannons.
USS Spirit (USS Spirit (NX-79995) at Memory Beta, the wiki for licensed Star Trek works), a prototype starship featured in the Ships of the Line 2009 calendar, also features rapid fire pulse phasers in it's arsenal, according to it's designer Mark Rademaker. 
The video game manual for Star Trek: Starfleet Command III describes the phaser cannon in great detail:
- "The Pulse Phaser is an advanced heavy weapon designed for a high rate of fire and a high damage yield ... The Pulse Phaser was developed by Starfleet as a weapon to combat future Borg incursions and was first fitted onto the prototype U.S.S. Defiant. The device functions similarly to a standard Phaser, but without a continuous beam. The energy emissions are instead stored in a magnetic field, allowing them to coalesce and agitate to higher energy states. The field is then redirected, forcing the burst of Phaser energy toward the target. This process is repeated rapidly using multiple magnetic field generators, and the result is a stream of phased energy projectiles. Although the range of such a weapon is much less than the standard Phaser due to rapid dissipation, from close range the pulse Phaser can do more damage than most Phaser types. The weapon has since been adapted to function on most Federation ships."
The video game Star Trek: Armada II also describes the phaser cannon as a pulse phaser on board Defiant-class ships, the Defiant-class variant Incursion-class (Incursion class at Memory Beta, the wiki for licensed Star Trek works) ships, Iwo Jima-class (Iwo Jima class at Memory Beta, the wiki for licensed Star Trek works) ships, Federation starbases, and pulse phaser turrets. The Klingon NuQ'DuJ-class (NuQ'Duj class at Memory Beta, the wiki for licensed Star Trek works) scoutships were also armed with this weapon.
According to the video game Star Trek: Elite Force II, the Sovereign-class USS Enterprise-E was also armed with a backup auxiliary twin pulse phaser cannon that was embedded into the primary hull. The cannon turret was capable of being manually operated by personnel in EVA suits.