"one, a or an, some," Old English ænig (adjective, pronoun) "any, anyone," literally "one-y," from Proto-Germanic *ainagas (source also of Old Saxon enig, Old Norse einigr, Old Frisian enich, Dutch enig, German einig), from PIE root *oi-no- "one, unique." The -y may have diminutive force here.

As a noun, late 12c.; as an adverb, "in any degree," c. 1400. Emphatic form any old______ (British variant: any bloody ______) is recorded from 1896. At any rate is recorded from 1847. Among the large family of compounds beginning with any-, anykyn "any kind" (c. 1300) did not survive, and Anywhen (1831) is rarely used, but OED calls it "common in Southern [English] dialects."

[A]ani refers to single entities, amounts, etc., occurring at random or chosen at random, as being convenient, suitable, to one's liking, etc. It is frequently emphatic and generalizing, having the force of 'any whatever, any at all' and 'any and every'. It is common in questions, conditional clauses, and negative statements, but not in affirmative statements (where som is used instead). [The Middle English Compendium]

"in any direction," 1610s, from any + whither.

"to any degree, in any way," c. 1200, from Old English ænige wisan, from any + wise (n.).

1911 as one word; two-word form is in Middle English (late 14c.); from any + place (n.).

"any longer, to any extent," one-word form by 1865, from any + more. Typically used with a negative, a custom as old as Middle English, where without any more is found late 14c.

"at whatever time," one-word form by 1854; two-word form is in Middle English (early 15c.; any while in the same sense is late 14c.), from any + time (n.).

c. 1300, ani-bodi, "any person," from any + body. One-word form attested by 1826. Phrase anybody's game (or race, etc.) is from 1840.

"in, at, or to any place," late 14c., from any + where. Earlier words in this sense were owhere, oughwhere, aywhere, literally "aught where" (see aught (n.1)).

"a thing," indefinitely, late Old English aniþing, from any + thing. But Old English ænig þinga apparently also meant "somehow, anyhow" (glossing Latin quoquo modo).

"any person or persons," 1844 as one word; since Old English as two words, from any + one. Old English also used ænigmon in this sense, Middle English eani mon, ani on; also compare anybody.