Middle English sho, "low-cut covering for the human foot," from Old English scoh, from Proto-Germanic *skokhaz (source also of Old Norse skor, Danish and Swedish sko, Old Frisian skoch, Old Saxon skoh, Middle Dutch scoe, Dutch schoen, Old High German scuoh, German Schuh, Gothic skoh). No known cognates outside Germanic, unless it somehow is connected with PIE root *skeu- "cover" (source also of second element in Latin ob-scurus).
The old plural form shoon lasted until 16c. The meaning "metal plate or rim nailed to the hoof of a horse or beast of burden to protect it from injury" is attested from c.1300. The distinction between shoe and boot (n.) is attested from c. 1400.
To stand in someone's shoes "see things from his or her point of view" is attested from 1767. Old shoe as a type of something worthless is attested from late 14c.
Shoes tied to the fender of a newlywed couple's car preserves the old custom (mentioned from 1540s) of throwing an old shoe at or after someone to wish them luck. Perhaps the association is with dirtiness, on the "muck is luck" principle.
1895, noun and adjective, in reference to a polish given to the shoes, especially by one who does so for pay; from shoe (n.) + shine (n.). Shoe-shine boy is attested by 1906. Earlier names for one who cleans and polishes shoes or boots for money include shoeblacker (1755), also shoeblack (1778), and shoeboy (1724).
also shoe-string, "string used to draw the sides of a shoe together and hold it firmly on the foot," 1610s, from shoe (n.) + string (n.). As figurative for "a small amount" it is recorded from 1882; hence, as an adjective, "operating at little cost" (1890). As a type of necktie from 1903; as a style of cooked potatoes from 1906.
lively Alpine folk dance, 1874, from German Schuhplattler, from schuh "shoe" (see shoe (n.)) + south German dialectal plattler, from platteln "to dance."