In 2368, Crewman Terry of the USS Sutherland replaced several power couplings. (TNG: "Redemption II") In the same episode, the Starboard power coupling of the Sutherland overloaded, causing a radiation leak on decks 10 through 12. This led Lt. Commander Hobson to take the phasers and photon torpedoes offline, in order to stop the radiation leak.
In 2373, an attack by the Tak Tak disabled the secondary power couplings on USS Voyager, preventing Captain Kathryn Janeway from accessing environmental controls to distribute an antigen to the macrovirus. (VOY: "Macrocosm")
In 2374, the Borg modified some power couplings on deck 8 of the USS Voyager. Though most of the Borg modifications to the ship were stripped away, Lieutenant B'Elanna Torres felt that these power couplings worked better with the modifications, so Captain Kathryn Janeway said to leave them as they were. (VOY: "Scorpion, Part II")
That same year, on stardate 51186.2, Seven of Nine reached into a primary power coupling with her bare hand during construction of the Voyager's astrometrics laboratory. She was quickly warned by Ensign Harry Kim that such action should not be taken again as they were in direct violation of Starfleet safety protocols. (VOY: "Revulsion")
On many Federation ships, including Voyager, power couplings played a critical role in the discharge of phaser energy from the phaser array. Aboard Voyager in 2373, after the Kazon hijacking, the primary phaser coil was disabled by Tom Paris and the backup coil sabotaged by crewman Lon Suder. Suder rigged the computer to block the discharge from the backup phaser coil, causing it to overload when the Kazon pirates attempted to fire. Their sabotage was successful, doing massive damage to the biologicals on the bridge and otherwise disabling the ship. (VOY: "Basics, Part II")