(covers information from several alternate timelines)
Jupiter (also known as Sol V) was the fifth and largest planet of the Sol system. The planet was noticeable for the Great Red Spot, its many moons, and bands of cloud layers. This gas giant was located near to the asteroid belt. (TOS: "The Changeling", "By Any Other Name"; VOY: "Future's End"; Star Trek: The Motion Picture; Star Trek Into Darkness)
In 2267, the position and orbital path of Jupiter were depicted on Chart 14A: The Sol System, stored in the USS Enterprise library computer. The chart was scanned by the probe Nomad in Auxiliary Control. (TOS: "The Changeling", production art)
In the mid-2270s, after one point eight hours from launch in Earth orbit, the Enterprise traveling at warp point five reached the Jovian system. The ship, staying close to the planet, passed through the system. Later, a star chart that labeled the location of Jupiter in a neighborhood of astronomical objects, stored in the Enterprise library computer, was scanned by V'ger. (Star Trek: The Motion Picture, production art)
In 2143, the NX-Alpha was destroyed near Jupiter shortly after breaking the warp 2 barrier. By 2151, Jupiter Station in orbit of Jupiter served as a repair facility to Earth Starfleet and the Earth Cargo Service. (ENT: "Silent Enemy", "Fortunate Son", "First Flight", et al.)
A close-up image of Jupiter was contained in the library computer aboard the USS Enterprise. This image was flashed on a viewscreen when the Talosians scanned the Enterprise computer in 2254. (TOS-R: "The Cage")
By the early 24th century a shuttle route had been established "from Jupiter to Saturn and back, once a day, every day," know as "the Jovian Run." Both Edward Jellico and Geordi La Forge used to pilot shuttles on this route early in their Starfleet careers. (TNG: "Chain of Command, Part II")
|The Sol System|
|Sol • Mercury • Venus • Earth (Luna) • Mars • Asteroid belt • Jupiter (Io; Ganymede) • Saturn (Mimas; Rhea; Titan) • Uranus • Neptune (Triton) • Pluto|
A painting seen in several episodes aboard the USS Enterprise-D was originally created by Rick Sternbach to illustrate a (non-Trek) science fiction story called "The Anvil of Jove". As such, it depicts a plane-like craft tethered to a balloon, cruising the atmosphere of Jupiter. 
According to Star Trek: Star Charts (Pgs. 22, "United Federation of Planets I"), Jupiter was classified as a J-class planet. This planet was a charter member of the United Federation of Planets in 2161.
Jupiter is one of the planets seen in the opening sequence of Star Trek: The Next Generation beside the Earth, Luna, Sol, and Saturn, shortly before the Enterprise-D started its exploration of the unknown space.