"light carriage with four wheels and seats for two," 1773, of unknown origin. OED finds no grounds for derivation from Hindi bagghi "a gig" or another Anglo-Indian source. Extended to baby carriages by 1884.
"sodomite," 1550s, earlier "heretic" (mid-14c.), from Medieval Latin Bulgarus "a Bulgarian" (see Bulgaria), so called from bigoted notions of the sex lives of Eastern Orthodox Christians or of the sect of heretics* that was prominent there 11c. Compare Old French bougre "Bulgarian," also "heretic; sodomite."
Softened secondary sense of "fellow, chap," is in British English "low language" [OED] from mid-19c. Meaning "something unpleasant, a nuisance" is from 1936. Related: Buggerly.
* The religious heretics in question were the Bogomils, whose name is a Slavic compound meaning "dear to God" (compare Russian bog "god") and might be a translation of Greek theophilos.
Meaning "cheap, raw whiskey" is attested from 1781, also sometimes "gin." Lightning bug "firefly, phosphorescent beetle" is attested from 1778. Lightning rod from 1790.
U.S. territory organized 1854, admitted as a state 1867, from a native Siouan name for the Platte River, either Omaha ni braska or Oto ni brathge, both literally "water flat." The modern river name is from French rivière platte, which means "flat river." Related: Nebraskan.
Bug eaters, a term applied derisively to the inhabitants of Nebraska by travellers on account of the poverty-stricken appearance of many parts of the State. If one living there were to refuse to eat bugs, he would, like Polonius, soon be "not where he eats but where he is eaten." [Walsh, 1892]