(covers information from several alternate timelines)
This page contains information regarding new Star Trek material, and thus may contain spoilers.
A supernova, occasionally shortened to nova, was rare and powerful explosions that typically occurred upon the death of a massive star. They had a burst radius, and burned out supernovae resulted in supernova remnants and concussion rings.
Supernovae were known to create subspace shock waves capable of collapsing a warp field, and an electromagnetic pulse capable of knocking out computers in the system. (VOY: "The Q and the Grey"; TNG: "11001001") They also produced severe theta radiation. (VOY: "The Omega Directive")
A star went supernova once every second in the universe. Within the Milky Way Galaxy, supernovae generally occurred approximately once per century. Up until 2373, only two Starfleet crews had ever witnessed supernovae firsthand. That year, a third observation was made by USS Voyager, setting the record for the closest observation at less than ten billion kilometers. (DIS: "Perpetual Infinity"; VOY: "The Q and the Grey")
In 2236, Alpha Lupi went supernova. As part of the Daedalus Project, Section 31 stationed Mike and Gabrielle Burnham at the nearby outpost Doctari Alpha so they could harness the energy for experiments with the red angel suit. They were believed killed in a Klingon terror raid, and for years after, their daughter believed that she had caused her parents death by convincing them to remain at the to witness the supernova rather than go on vacation to Mars. (DIS: "Will You Take My Hand?", "The Red Angel", "Perpetual Infinity")
In 2269, Beta Niobe went supernova, resulting in the destruction of planet Sarpeidon. Its inhabitants had been aware that this was going to happen for a long time, and had evacuated. The Enterprise's crew, having calculated the time of the event in advance, observed the supernova. (TOS: "All Our Yesterdays")
In 2364, a star in the Beta Magellan system exploded releasing a supernova and a subspace shock wave. The shock wave released an electromagnetic pulse, resulting in main computer failure on Bynaus. The Bynars stole USS Enterprise-D with Captain Picard and Commander Riker still on board. Picard and Riker managed to get the system rebooted and returned the Enterprise to Starbase 74. (TNG: "11001001")
In 2366, the star Beta Stromgren exploded as a supernova. The last stages of the star's life were observed by the Enterprise-D while making first contact with the spaceborne entity Gomtuu, which, also aware of the impending event, had come there to die. (TNG: "Tin Man")
In 2370, Jadzia Dax warned Gideon Seyetik that his plan to use protomatter to re-ignite the dead star Epsilon 119 might inadvertently unleash a supernova instead. Seyetik brushed this off, quipping that "nothing of any worth was ever created by a pessimist." The star was re-ignited successfully. (DS9: "Second Sight")
In 2373, the Q Civil War caused hazardous repercussions throughout the Milky Way Galaxy, including "galactic crossfire" in the form of supernovae. At least three supernovae went off within three days in a single sector of the Delta Quadrant. It was explained to Chakotay, by a female Q, that "each time [one of these stars] implodes, a negative density false vacuum is created, which actually sucks the surrounding matter into the Continuum." The crew of Voyager, acting on information provided by the female Q, used the explosion of one of these supernovae to enter the Continuum themselves in order to rescue Q and Captain Janeway. (VOY: "The Q and the Grey")
Several weeks later, in the Alpha Quadrant, a Changeling posing as Doctor Julian Bashir attempted to trigger a supernova in the Bajoran sun using trilithium, tekasite, and protomatter. The Founder was stopped by Kira Nerys, Jadzia Dax, and the crew of the USS Defiant. (DS9: "By Inferno's Light")
In 2387, the Romulan sun threatened to go supernova, endangering the galaxy. Ambassador Spock prepared an attempt to stop the supernova by using red matter to create a black hole, which he hoped would consume the supernova. Before he could enact this plan, however, the star exploded and destroyed Romulus. Spock still used the red matter to stop the supernova after Romulus was gone, but this led to the creation of the alternate reality. In 2258 of the alternate reality, Spock used a mind meld to demonstrate the supernova event to the alternate James T. Kirk. (Star Trek, PIC: "Remembrance")