A rainbow is an optical and meteorological phenomenon caused by precipitation in an atmosphere having a prismatic effect upon white light (typically from a sun), and creating the appearance of an arc of color through the sky.
Despite being able to explain its origins, Spock never contemplated the beauty of a rainbow before succumbing to the effects of the Omicron spores in 2267. (TOS: "This Side of Paradise")
In 2364, while suffering from polywater intoxication, Geordi La Forge bemoaned never having seen a rainbow as Doctor Beverly Crusher administered a hypospray. (TNG: "The Naked Now")
In 2370, Gideon Seyetik painted the following mental picture of Da Vinci Falls for Benjamin Sisko: "Imagine...Water cascading off cliffs the height of Mount Everest and thundering through continuous rainbows, straight into an ocean the color of sapphire wine." (DS9: "Second Sight")
In Irish legend, a leprechaun's pot of gold was to be found at the end of a rainbow's arch. In 2376, when Fair Haven inhabitant Seamus asked Tom Paris how to find the pot of gold in Glen Abbey, Paris told him to follow the rainbow. (VOY: "Spirit Folk")
The 1960s Earth band Berman's Rainbow Dreamers took their name from the rainbow, alluding to its multicolored nature in their psychedelic imagery and aesthetic. (DS9: "Past Tense, Part II")
Two songs performed by Vic Fontaine featured rainbows in the lyrics: "It's Only a Paper Moon" and "I've Got the World on a String". (DS9: "It's Only a Paper Moon")
What appeared to be a structure resembling a rainbow was visible outside the Daystrom Institute in Okinawa in 2399. (PIC: "Remembrance")