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 as rain (blessings, tears, etc.) is recorded from 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, 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 on an exposed roof?) Probably rather an extension of cats and dogs as proverbial for "strife, enmity" (1570s).