Galileo

There have been several Starfleet shuttlecraft assigned the name Galileo, and is often assigned to the various incarnations of the USS Enterprise.

Galileo (I)
The Galileo was a Class F shuttlecraft assigned to the USS Enterprise in the 2260s. In 2267, Lieutenant Commander Spock led a small scientific team aboard the Galileo to chart the Murasaki 312 quasar. During the survey, the Galileo crashlanded on the planet Taurus II, and many systems were destroyed. Fortunately, they managed to get the shuttle into orbit and were beamed aboard the Enterprise before the shuttle burned up in Taurus II's atmosphere. (TOS episode: "The Galileo Seven").

Galileo (II)
Following the destruction of the original Galileo, a new Galileo with the same registry was assigned to the Enterprise. In 2267, Captain James T. Kirk, Spock, and Dr. McCoy used the Galileo to transport Nancy Hedford back to the Enterprise from Epsilon Canaris III. A few months later, the Galileo transported Ambassador Sarek and Amanda Grayson to the Enterprise for the Babel Conference. (TOS episodes: "Metamorphosis" and "Journey to Babel").

In 2268, the Galileo was nearly destroyed when Commander Spock used her to travel inside a giant space amoeba to destroy it. Spock's mission was successful, and the shuttle was threw clear and collected and repaired by the Enterprise. A few weeks later, Captain Kirk and a small party used the Galileo to proceed on a diplomatic mission to Tarsus IV. Enroute back to the Enterprise, the Galileo was brought off course to a medieval planet nearby. Unable to control the shuttle, it crashlanded on the surface of the planet, and while the occupants survived the Galileo was damaged beyond repair. (TOS episode: "The Immunity Syndrome" and comic: "Day of the Inquisitors").

Galileo II (NCC-1701/7)
Following the destruction of the second Galileo, a new Class F shuttle named the Galileo II was assigned to the Enterprise. In 2269, Dr. Stevrin and his followers stole the Galileo II for part of their quest in finding Eden. The Galileo II was later recovered by the Enterprise. (TOS episode: "The Way to Eden").

Galileo (NCC-1701-A/05)
The Galileo was a Type-1 shuttlecraft assigned to the USS Enterprise-A upon its launch in 2286. In 2287, Captain Kirk used the Galileo to transport a team down to Nimbus III to rescue the hostages that Sybok and his followers had taken in Paradise City. Sybok was able to overcome Kirk's forces and together they returned to the Enterprise, where the Galileo was badly damaged during an emergency landing in the shuttlebay. (TOS movie: Star Trek V: The Final Frontier).

Galileo (NCC-1701-D/07)
The Galileo was a Type-6 shuttlecraft assigned to the USS Enterprise-D in the 2360s. In 2364, Lieutenant Natasha Yar used the Galileo to transport Captain Jean-Luc Picard aboard the Enterprise for the first time. (TNG episode: "All Good Things...").