"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). [Middle English Dictionary]