Interphase Cloaking Device
The Interphase Cloaking Device was an advanced type of cloaking device that allows a starship to travel through solid matter and high-energy fields. A Molecular Phase Inverter moves the ship out of phase with the spacetime continuum.
In 2358, a branch of Starfleet Intelligence illegally developed such a device in direct violation of the Treaty of Algeron, which explicitly banned the Federation from developing cloaking technology.
The illegal actions and the fact that it was referred to as "a secret division of Starfleet Intelligence" suggests that the 'branch' may have been Section 31. (ENT: "These Are the Voyages...")
A test aboard the USS Pegasus was initially successful, but the crew mutinied against the Captain, Erik Pressman, when they realized that what he was doing violated the Treaty of Algeron. William T. Riker, an ensign at the time, defended his captain, and the two of them along with seven others succeeded in escaping the ship.
Shortly thereafter, a temperature spike in the plasma intercoolers caused an explosion which led Captain Pressman and Ensign Riker to believe the ship had been destroyed. In fact it had not, and it drifted into an asteroid field in the Devolin System, and after drifting into asteroid Gamma 601 in that field, the interphase cloak failed, causing the ship to rematerialize half sticking out of a cavern in the asteroid.
Starfleet Intelligence attempted to cover the incident up, but the truth was revealed in 2370 when Pressman attempted to recover the device. (TNG: "The Pegasus")
Several other races have either experimented with, or utilize interphasing technology:
The Romulans were experimenting with an molecular phase inverter to create an interphase cloak. The experiment failed, heavily damaging the vessel on which the experiment was being run. The Klingons also experimented with interphase cloaking technology in the early 2360s but they abandoned their research because of several accidents. (TNG: "The Next Phase").
Interphase technology was used extensively by the Srivani to hide their scientific experiments. (VOY: "Scientific Method") The Voth also used interphase cloaking technology. This allowed Forra Gegen and Veer to covertly observe the USS Voyager and her crew. (VOY: "Distant Origin")