Middle English rein, from Old English regn "rain, descent of water in drops through the atmosphere," from Proto-Germanic *regna- (source also of Old Saxon regan, Old Frisian rein, Middle Dutch reghen, Dutch regen, German regen, Old Norse regn, Gothic rign "rain"), with no certain cognates outside Germanic, unless (Watkins) it is from a presumed PIE *reg- "moist, wet," which may be the source of Latin rigare "to wet, moisten" (see irrigate), but de Vaan doesn't suggest Germanic cognates for the Latin word.

Rain dance "dance performed by a tribal group in hope of summoning rain" is from 1867; rain date in listings for outdoor events, giving an alternative date should rain interrupt them on the intended day, is from 1948. To know enough to come in out of the rain (usually with a negative) "take ordinary measures for one's protection" is from 1590s. Rain-shower is Old English renscur. Rain-gauge "instrument for collecting and measuring the amount of rainfall at a given place" is by 1769.

"fall in drops through the air," Middle English reinen, from Old English regnian, usually contracted to rinan; see rain (n.), and compare Old Norse rigna, Swedish regna, Danish regne, Old High German reganon, German regnen, Gothic rignjan. Related: Rained; raining. Transferred and figurative use, of other things that fall in showers or drops (blessings, tears, etc.), is by c. 1200.

To rain on (someone's) parade is attested from 1941. Phrase to rain cats and dogs is attested from 1738 (variation rain dogs and polecats is from 1650s), of unknown origin and signification, despite intense speculation. One of the less likely suggestions is pets sliding off sod roofs when the sod got too wet during a rainstorm. Cats dropping from roofs while night-prowling was an occasional literary trope, but there is likely no literal meaning in the expression. Probably it is an extension of cats and dogs as proverbial for "strife, enmity," which is attested by 1570s.

also raincloud, "cloud from which rain falls," 1800, from rain (n.) + cloud (n.).

also rain out, rainout, "cancellation or interruption of an outdoor event due to rain," 1947, from the verbal phrase; see rain (v.) + out (adv.). Of baseball games, to be rained out "cancelled because of rain" is attested from 1928.

also rainproof, "not admitting the entrance of rain or penetration by it," 1788, from rain (n.) + proof (n.).

"dense forest in an area of high rainfall with little seasonal variation," 1899, apparently a loan-translation of German Regenwald, coined by A.F.W. Schimper for his 1898 work "Pflanzengeographie."

"arc of prismatic colors formed by the refraction of light rays by drops of rain or vapor," Middle English rein-bowe, from Old English renboga; see rain (n.) + bow (n.). Common Germanic compound (Old Frisian reinboga, Old Norse regnbogi, Swedish regenbåge, Dutch regenboog, German Regenbogen). The American rainbow trout (1876) is so called for its resplendent colors. Old English also had scurboga "shower-bow."

word-forming element meaning "rain, rainfall; excessive moisture," from Greek ombros "shower of rain," from PIE *ombh-ro- "rain" (source also of Sanskrit abhra "cloud, thunder-cloud, rainy weather," Latin imber "rain, heavy rain; rainwater"), from root *nebh- "moist; water" (see nebula). 

also rain-fall, by 1850 as "amount of precipitation that falls as rain, from rain (n.) + fall (n.). By 1858 as "a falling of rain."

1650s, "pertaining to rain," from French pluvial (12c.), from Latin pluvialis "of or pertaining to rain, rainy, rain-bringing," from (aqua) pluvia "rain (water)," from fem. of pluvius "rainy," from plovere "to rain," from PIE root *pleu- "to flow." Middle English pluvious "rainy" is attested from mid-15c., from Latin pluviosus. In geology, "depending on or arising from the action of rain," by 1859.