The emergency channel was a block of communications channels reserved by Starfleet for emergency use. Starfleet personnel could use this channel to transmit a plea for help or a status update after a ship or station was disabled or non-communicative.
In 2285, the USS Enterprise approached the fast-approaching USS Reliant. Admiral James T. Kirk attempted to contact the Reliant using the emergency channel. The Reliant, however, had actually been commandeered by Khan Noonien Singh, who responded by claiming that the Reliant's chambers coil had overloaded the ship's comm system. Further sensor scans revealed that their coil emissions were normal before the Reliant unleashed a devastating attack on the Enterprise. (Star Trek II: The Wrath of Khan)
Later in 2285, Kirk and his bridge crew attempted to steal the Enterprise from the Earth Spacedock. Admiral Morrow, the Commander, Starfleet, hailed Kirk on the emergency channel to order him to surrender the Enterprise. Kirk offered no reply. (Star Trek III: The Search for Spock)
In 2286, the Whale Probe disabled two starships. One of these ships, the USS Yorktown, sent a message on emergency channel 0130 to Starfleet Command. Captain Joel Randolph informed Command that his ship had lost all power. He hoped that his chief engineer could restore power to his ship through a makeshift solar sail. As the probe approached Earth, it disabled Spacedock in a similar fashion. Spacedock attempted to contact Starfleet Command on the emergency channel to inform them they had lost all internal power. (Star Trek IV: The Voyage Home)
In 2287, after the USS Enterprise-A had been hijacked by Sybok and his band of followers, Kirk, Captain Spock and Doctor Leonard McCoy broadcast a message on the emergency channel calling for assistance. Their message was intercepted by Klaa's Bird-of-Prey, who claimed that they were Starfleet Command receiving the message. (Star Trek V: The Final Frontier)
In 2371, Quark contacted the USS Defiant from Deep Space 9 on the emergency channel (much to the annoyance of Major Kira Nerys) to remind Commander Benjamin Sisko about how Grand Nagus Zek had played a pivotal role in establishing contact with the Dominion prior to his meeting with Starfleet Command. The nagus was also interested in the release of his nephew Belongo from Starfleet authorities on Aldebaron III and wished to call in a favor with Sisko. (DS9: "Past Tense, Part I")
In 2376, Lieutenant Reginald Barclay attempted to contact the USS Voyager in grid 10, sector 3658 of the Delta Quadrant from the Communications Research Center on the emergency channel using the MIDAS array. This was Voyager's first two-way communication with Starfleet since becoming stranded in the Delta Quadrant in 2371. (VOY: "Pathfinder")