(covers information from several alternate timelines)
A gas giant is a huge planet made entirely of base gases, including fluorine, methane, and ammonia. They do not possess a solid surface, but rather have dense atmospheres. These turbulent atmospheres are generally made of the same materials as stars, however, they lack the mass necessary to begin nuclear fusion. Theoretically, if two gas giants collide, they may create an object capable of a self-sustaining fusion reaction, leading to the birth of a new star.
There were several types of gas giants known to Humans: class J, class 6, class 7, and the class 9 gas giant, which was also known to the Klingons as the Q'tahL class. (DS9: "Starship Down"; ENT: "Broken Bow", "Sleeping Dogs")
The Sol system had four gas giants, Jupiter, Saturn, Uranus, and Neptune, none of which were class 9. (TOS: "The Changeling", ENT: "Sleeping Dogs")
The Andorians and Aenar's homeworld of Andoria was a moon that orbited a ringed gas giant.
Gas giants generate intense magnetic fields that often create unique waveforms. The resulting EM interference sounds very strange when played over speakers. Travis Mayweather referred to these sounds as "siren calls," noting that while he lived aboard the ECS Horizon as a kid, his dad would put them through the speakers whenever they flew by a gas giant. (ENT: "Sleeping Dogs")
Neelix's cousin once had a job transporting disulfides from a gas giant. He enjoyed the turbulence, according to Neelix, who also noted that "disulfides are known to cause delusions." (VOY: "Friendship One")
In 2152, Enterprise NX-01 pulled the IKS Somraw from a class J gas giant. (ENT: "Sleeping Dogs", "Marauders", "Judgment") Later that year, they encountered a gas giant in Arkonian space that had "dozens of moons," and was referred to as "like a gravitational jigsaw puzzle." (ENT: "Dawn")
The Xindi-Insectoid shuttlecraft discovered in 2154 was discovered to have almost half of its power grid routed to structural integrity, leading the crew of Enterprise to theorize that it could probably be flown inside a gas giant. (ENT: "Hatchery", "Azati Prime")
In the mirror universe, the Tholians held the USS Defiant at a facility in the Vintaak system that was orbiting the system's lone gas giant. (ENT: "In a Mirror, Darkly")
In 2369, the USS Enterprise-D was able to witness the collision of two gas giants in the Detrian system. (TNG: "Ship in a Bottle")
Also around this time, Rudolph Ransom eluded a Romulan Warbird by taking his vessel into the atmosphere of a gas giant. (VOY: "Equinox, Part II")
In 2370, the USS Raman became trapped in the atmosphere of a gas giant while the crew was attempting to sample it at a low orbit. (TNG: "Interface")
In 2371, a Maquis interceptor, piloted by the Female Changeling, lured a runabout, piloted by Kira Nerys and Odo, to a moon orbiting the gas giant located near the Badlands. (DS9: "Heart of Stone")
In 2376, the Delta Flyer encounter a class T gas giant within a stellar nursery in the Delta Quadrant. It was surrounded by rings, one of which radiogenic, and Janeway used these particles to reinitialize warp power in the Flyer following a massive antimatter loss. The Flyer and its occupants were later discovered orbiting the gas giant by the USS Voyager. (VOY: "Good Shepherd")
During the Antarian Trans-stellar Rally in 2377, one of the competing ships changed course by using the gravity from a gas giant to boost its speed, and successfully made up for lost ground. (VOY: "Drive")