Two incidences where military aircraft have actually shot themselves down or caused damage severe enough to have to land the aircraft.

The Netherlands’ Defense Safety Inspection Agency (Inspectie Veiligheid Defensie) is investigating an incident during a January military exercise in which a Dutch Air Force F-16 was damaged by live fire from a 20-millimeter cannon, It’s OWN 20-millimeter cannon. At least one round fired from the aircraft’s M61A1 Vulcan Gatling gun struck the aircraft as it fired at targets on the Dutch military’s Vliehors range on the island of Vlieland, according to a report from the Netherlands’ NOS news service.
Two F-16s were conducting firing exercises on January 21, 2019. It appears that the damaged aircraft actually caught up with the 20mm rounds it fired as it pulled out of its firing run. At least one of them struck the side of the F-16’s fuselage, and parts of a round were ingested by the aircraft’s engine. The F-16’s pilot managed to land the aircraft safely at Leeuwarden Air Base.
The incident reflects why guns on a high-performance jet are perhaps a less than ideal weapon. The Vulcan M61A1 six-barrel Gatling gun and its linkless ammunition feed system is capable of firing over 6,000 shots per minute, but its magazine carries only 511 rounds, just enough for five seconds of fury. The rounds have a muzzle velocity of 3,450 feet per second (1050 meters per second). That is speed boosted initially by the aircraft itself, but atmospheric drag slows the shells down eventually. And if a pilot accelerates and maneuvers in the wrong way after firing the cannon, the aircraft could be unexpectedly reunited with its recently departed rounds.

 

 

https://arstechnica.com/tech-policy/2019/04/dutch-f-16-takes-cannon-fire-from-itself/

During flight testing on September 21, 1956, a U.S Navy Grumman F-11 Tiger flying from Grumman’s test facility in Riverhead, New York fired a burst from four Colt Mk. 12 20mm cannons, entered a steep dive, kicked in the jet’s afterburners, and went supersonic, when suddenly the windshield blew in and mortally wounded the engine. The F-11 Tiger, like all Grumman aircraft, was named after a cat. Fast and nimble, the F-11 was only the second supersonic fighter in the Navy's inventory, capable of 843 miles per hour (Mach 1.1).
The plane was actually Grumman's first supersonic fighter, and the company's inexperience with the consequences of supersonic flight, as well as the fighter's amazing speed, would be one test Tiger's undoing. A Grumman test pilot flying a Tiger off the coast of Long Island dropped his nose 20 degrees and pointed it at an empty spot of ocean. He fired a brief, four second burst from his four Colt Mk.12 20-millimeter cannons, entered a steeper descent, and hit the afterburners.
A minute later, his windshield suddenly caved in and his engine started making funny noises, eventually conking out as the pilot attempted to return to Grumman's Long Island airfield.
The test pilot had assumed he had been the victim of a bird strike, but the accident investigation revealed another cause: In his fast descent, the pilot had actually flown into his own stream of 20-millimeter cannon rounds.
Although the rounds had a head start (the air speed of the aircraft, plus the muzzle velocity of the rounds) they slowed quickly due to drag passing through the surrounding air. The rounds decelerated, the Tiger accelerated, and the two reunited in the sky, with fatal (for the aircraft) consequences.
The Tiger was totaled during the crash and the pilot, while severely injured, was able to return to flight status less than six months later. The Navy only purchased 200 Tigers, and withdrew them from service once faster, better planes like the F-8 Crusader and F-4 Phantom II entered the fray.
The Navy's Blue Angels flight demonstration team flew the F-11 Tiger until 1969.

 

https://www.popularmechanics.com/military/aviation/a27967/the-fighter-plane-that-shot-itself-down/