But Tolkien didn’t invent this word. It was used much earlier by Sir Walter Scott (where Tolkien may have encountered it), among many other instances. So what is a wraith, actually? What does this rather curious word mean? It’s usually used for some sort of ghost, apparition, or premonitory omen of death (something like the Grim in J.K. Rowling) as here.
But regardless of how it’s used, what does it mean? For the best sense of that, we have to turn to its etymology. Yet as you can see at Encarta — “[Early 16th century. Origin ?]” — its etymology is not terribly obvious. So let’s look a bit further back. In his influential Etymological Dictionary of the English Language, Walter Skeat can only conjecture (see the illustration at the top of this post). One suggestion connects it to Icelandic vörðr “warden, guardian” .
What else do we have? How about John Trotter Brockett’s Glossary of North Country Words? And no, I’m not making up Brockett’s middle name — something that would have tickled Tolkien’s fancy, I imagine! Brockett connects wraith to a northern dialectal word, waff, meaning “an apparition in the exact resemblance of a person, supposed to be seen just before or soon after death.” He guesses the word may be linked to waft, no doubt envisioning the airy apparition wafting along in a gentle breeze on the moors. 
Poking around in various other etymological dictionaries, we find other suggestions, some good, some not so good — including Old English weard, ward “warden, guardian” (cf. Skeat’s vörðr); Old Gaelic breith (aspirated form, bhreith) “doom, judgment”; and even Modern English wrath, wroth (from Old English wráð), suggesting a wraith might be a particularly wrathful spirit. The OED traces the word all the way back to 1513, to a translation of the Aeneid made by the Scottish poet, Gavin Douglas; consequently, they assume its origin to be Scottish. 
Any or all of these are possible, but Tolkien had a different etymology in mind. He thought wraith might have been a form of the verb writhe “to twist or struggle, as in pain”, with the archaic past participle, writhen (< Middle English writhen < Old English wríðen “to twist, torture”). The idea being that a wraith was something twisted, contorted, bent out of its proper original shape — in the case of the Nazgûl, by evil. 
This would, in fact, cousin the word to wrath, wroth, which has a literal meaning closer to “twisted by rage” than is usually remembered. Its Old English form was wráð, derived from Primitive Germanic *wraithaz. Now that's beginning to look familiar!
Other interesting cognates include Gothic wraiqs “curved, winding, twisting”, and perhaps wraka “persecution, punishing pursuit; Old Frisian wreth “evil”; Old Saxon wred, Middle Dutch wret “cruel”; Old High German reid, Old Norse reiðr “wroth”; Old Norse ríða “to twist, knit, wind” — all originally related to the Proto-Indo-European root *wreit “to turn, wind”. Another descendent of this root is Modern English wreath, from Old English wriða “band (i.e., that which is wound around)” — sounds rather like a ring, no? Indeed, in the Old English corpus, wríða is sometimes used for “ring” (as in the Homilies).
From “wraith” to “ring” in only, what, a dozen complicated steps? :) And I'm not even remotely finished with this topic! Stay tuned for more to come.
 Skeat, Walter W. An Etymological Dictionary of the English Language. 2nd ed. Oxford: Clarendon, 1893, p. 720.
 Brockett, John Trotter. A Glossary of North Country Words with Their Etymology and Affinity to Other Languages and Occasional Notices of Local Customs and Popular Superstitions. 3rd ed. Newcastle Upon Tyne: Emerson, Charnley, Bigg Market; and Simpkin, Marshall, & Co., 1846, pp. 200-1, 202.
 Gilliver, Peter, Jeremy Marshall, and Edmund Weiner. The Ring of Words: Tolkien and The Oxford English Dictionary. Oxford: Oxford University Press, 2006, pp. 223-4.
 Shippey, Tom. The Road to Middle-earth: How J.R.R. Tolkien Created a New Mythology. Rev. and expanded ed. Boston: Houghton Mifflin, 2003, pp. 148-50.