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 it is from a presumed PIE *reg- "moist, wet," which may be the source of Latin rigare "to wet, moisten" (see irrigate).
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. (Ever see a dog react to a rainstorm by climbing up an exposed roof?) Probably rather an extension of cats and dogs as proverbial for "strife, enmity" (1570s).