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(covers information from several alternate timelines)
A gravity well is a distortion of the space-time continuum caused by an object with mass, which can be conceptualized on a two-dimensional surface as a depression: the "well". The curvature of the well corresponds to gravity.
In 2155 in the mirror universe, the Tholians detonated a tricobalt warhead in the gravity well of a dead star, which created an interphasic rift into another universe in the future of 2268. (ENT: "In a Mirror, Darkly"; TOS: "The Tholian Web")
In 2258 of the alternate reality, the Constitution-class starship USS Enterprise became caught in the gravity well of a black hole created by the explosion of a massive amount of red matter when the Jellyfish crashed into the Narada. Fortunately, the Enterprise managed to escape the gravity well after Montgomery Scott ejected the ship's multiple warp cores and detonated them, creating a large blast wave that pushed the ship out of danger. (Star Trek)
The Bajoran wormhole had its own gravity well. After a carrier wave emitted from the newly-established wormhole relay station created a subspace inversion in the wormhole in 2371, its gravity well increased by a factor of three. (DS9: "Destiny")
In 2368, Wesley Crusher and the Nova Squadron flew in a diamond slot formation around Saturn and came out of the gravity well of Saturn's moon Titan, shortly before the Squadron suffered a catastrophic accident after attempting the dangerous maneuver Kolvoord Starburst, which claimed the life of Joshua Albert. (TNG: "The First Duty")
The Dyson sphere had an immense gravity well, not least due to the star at its center but the mass of the structure itself. As no radiant sunlight light or solar wind escaped from the sphere, starships were not able to detect the sphere until they were almost on top of it. As a result the sphere's gravity well came as quite a shock to both the USS Jenolan in 2294 and USS Enterprise-D in 2369, so much so that the former was pulled in and crashed on the surface. (TNG: "Relics")
Later on, in a holodeck simulation, a holographic James Moriarty took control of the Enterprise-D and the ship became trapped in the gravity well of a gas giant in the Detrian system. To fool Moriarty into releasing the voice commands and regain command, Jean-Luc Picard created a holographic program, Picard Delta One to make Moriarty think he had left the Enterprise on the shuttlecraft Sakharov. (TNG: "Ship in a Bottle")
In 2369, two quantum singularity lifeforms came into this space-time continuum to save their young who were trapped in an artificial gravity well, the engine core of the Romulan warbird. The aliens needed a natural gravity well to incubate their young and thought the engine core was a natural one. (TNG: "Timescape")
In 2370, Commander Benjamin Sisko ordered Gideon Seyetik to turn his shuttlepod around and return to the USS Prometheus. Seyetik told Sisko that it was told late, as he had entered the gravity well of the dead star Epsilon 119. He later died after his shuttlepod crashed on Epsilon 119, but the star was re-ignited with the use of protomatter. (DS9: "Second Sight")
In 2374, Tuvok and Seven of Nine were captured by the Hirogen. However, the ship they were on was slowly being sucked in by a black hole. On the USS Voyager, the crew tried beaming them off but Harry Kim warned Kathryn Janeway that the gravity well from the black hole could scatter their patterns. Janeway saw no other choice and was ulitmately successful in beaming them onto Voyager. (VOY: "Hunters")
It was also possible that while a planet may be found inside a rift that has the properties of a gravity well, the gravity on the planet's surface may be similar to Earth's. Tom Paris and Tuvok were stranded on such a planet while USS Voyager was nearly pulled inside a rift containing the planet. (VOY: "Gravity")