[hindmost part of an animal] Old English tægl, tægel "posterior extremity," from Proto-Germanic *tagla- (source also of Old High German zagal, German Zagel "tail," dialectal German Zagel "penis," Old Norse tagl "horse's tail," Gothic tagl "hair"), according to Watkins from PIE *doklos, from suffixed form of root *dek- (2) "something long and thin" (referring to such things as fringe, lock of hair, horsetail; source also of Old Irish dual "lock of hair," Sanskrit dasah "fringe, wick").
According to OED (2nd ed., 1989), the primary sense, at least in Germanic, seems to have been "hairy tail," or just "tuft of hair," but already in Old English the word was applied to the hairless "tails" of worms, bees, etc. But Buck writes that the common notion is of "long, slender shape."
Extended to many things resembling a tail in shape or position; by late 14c. as "hinder, bottom, or concluding part" in space or time of a text, a storm, etc. As an adjective from 1670s.
The meaning "reverse side of a coin" (opposite the side with the head) is from 1680s. Of descending strokes of letters, from 1590s. Tails "coat with tails" is from 1857, short for tail-coat.
To turn tail "wheel about, take flight" (1580s) seems to have been originally a term in falconry. The image of the tail wagging the dog is attested by 1866, American English, perhaps inspired by a much-reprinted 1863 newspaper joke:
Why does a dog wag his tail?
Because the dog is stronger than the tail; otherwise the tail would wag the dog.
[Woodcock, Illinois, Sentinel, Sept. 2, 1863]
Another Old English word for "tail" was steort (see stark). The slang sense of "pudenda" is from mid-14c.; that of "woman as sex object" is from 1933, earlier "act of copulation" with a prostitute (1846).