Old English cropp "head or top of a sprout or herb, any part of a medicinal plant except the root," also "bird's craw" (the common notion is "protuberance"), cognate with Old High German kropf, Old Norse kroppr.
"The word has a remarkable variety of special senses ..." [Century Dictionary]. OED writes that "OE. had only sense 1. 'craw of a bird' and 3. 'rounded head or top of a herb'; the latter is found also in High German dialects (Grimm, Kropf, 4c); the further developments of 'head or top' generally, and of 'produce of the field, etc.' appear to be exclusively English."
Meaning "grain and other cultivated plants grown and harvested" (especially "the grain yield of one year") is from early 14c. (in Anglo-Latin from early 13c.). Probably this sense development is via the verbal meaning "cut off the top of a plant" (c. 1200).
From the notion of "top" comes the sense "upper part of a whip," hence "handle of a whip" (1560s), hence "a kind of whip used by horsemen in the hunting field" (1857). "It is useful in opening gates, and differs from the common whip in the absence of a lash" [Century Dictionary].
General sense of "anything gathered when ready or in season" is from 1570s. Meaning "a thick, short head of hair" is from 1795. Meaning "top or highest part of anything" is from late 14c. In Middle English crop and rote "the whole plant, crop and root," was figurative of totality or perfection. Crop-circle is attested by 1974.
c. 1200, "cut off the top of a plant," from crop (n.). Mid-14c. in reference to animals feeding on plants. The general meaning of "to cut off" is attested from mid-15c. Meaning "cut off a part of (the ear of an animal) as a mark of identification is from c. 1600. In reference to clipping of cloth, by 1711. Women's fashion crop top is attested from 1984.
With up, "to sprout, appear apparently without design from below the surface" is from 1844, said by OED to be from an earlier use in mining in reference to veins of ore or strata of rock, "come to the surface, become visible on the ground" (1660s). Related: Cropped; cropping.
"a fall, as in horseback riding, in which the rider is thrown over the horse's head," hence "a failure," 1858, perhaps from crop (n.) in the "top of the head" sense.
1690s, originally an art criticism term, "assemblage of figures or objects forming a harmonious whole in a painting or design," from French groupe "cluster, group" (17c.), from Italian gruppo "group, knot," which probably is, with Spanish grupo, from a Germanic source, from Proto-Germanic *kruppaz "round mass, lump," part of the general group of Germanic kr- words with the sense "rounded mass" (such as crop (n.).
Extended to "any assemblage, a number of individuals related in some way" by 1736. Meaning "pop music combo" is from 1958. As it was borrowed after the Great Vowel Shift in English, the pronunciation of the -ou- follows French rather than English models.