the modern verb is a merger of two related Old English words. The first is rinnan, irnan (strong, intransitive, past tense ran, past participle runnen), from Proto-Germanic *renwanan (cf. Middle Dutch runnen, Old Saxon, Old High German, Gothic rinnan, German rinnen "to flow, run"), both from PIE *ri-ne-a-, nasalized form of root *reie- "to flow, run" (see Rhine). The sense of "cause to run" is from Old English ærnan, earnan (weak, transitive, probably a metathesis of *rennan), from Proto-Germanic *rannjanan, causative of the root *ren- "run."
Of streams, etc., from c.1200; of machinery, from 1560s. Meaning "to be in charge of" is first attested 1861, originally American English. Meaning "to seek office in an election" is from 1826, American English. Phrase run for it "take flight" is attested from 1640s. Most figurative uses are from horseracing or hunting (cf to run (something) into the ground, 1836, American English), except (to feel) run down (1901) which is from clocks (in the literal sense, 1761). To run across "meet" is attested from 1855, American English. To run short "exhaust one's supply" is from 1752; to run out of in the same sense is from 1713.
"spell of running," mid-15c. (earlier ren, late 14c.), from run (v.). Sense of "small stream" first recorded 1580s, mostly Northern English dialect and American English. Meaning "series or rush of demands on a bank, etc." is first recorded 1690s. Baseball sense is from 1856. Meaning "single trip by a railroad train" is from 1857. Military aircraft sense is from 1916. Meaning "total number of copies printed" is from 1909. Meaning "tear in a knitted garment" is from 1922. Phrase a run for one's money is from 1872 in a figurative sense, originally from horse racing, implying competition (1841). Run-in "quarrel, confrontation" is from 1905.