Quoth

“Though thy crest be shorn and shaven, thou,” I said, “art sure no craven,
Ghastly grim and ancient Raven wandering from the Nightly shore—
Tell me what thy lordly name is on the Night’s Plutonian shore!”
            Quoth the Raven “Nevermore.”

Edgar Allen Poe, The Raven

Etymology

By a happy coincidence, quoth looks a bit like quote, and so most people have little trouble understanding the phrase "quoth the raven" (and the context helps too).

But quote is unrelated to quoth. Quote traces back to the Latin word quot meaning "how many", while quoth traces back to cweþan meaning "to say".

Quoth is the past tense of quethe. Quethe is a defective verb, i.e. a verb that has lost some of its forms. The only form of quethe that is still in use in modern English is its past tense (i.e. quoth). No one ever quethes anything or is seen to be quething anything anymore.

Defective verbs

English has a few other defective verbs as well. Primarily, modal verbs (like can, may, must, shall) can only appear in certain places. "I can do it" is roughly equal to "I am able to do it", but while "I will be able to do it" is a valid sentence, "I will can do it" is not. Similarly, "beware the dog" is still commonly said, but bewares, bewared, and bewaring have all but gone from modern English.

The Raven features another verb that can be called defective as well:

Then, methought, the air grew denser, perfumed from an unseen censer
Swung by Seraphim whose foot-falls tinkled on the tufted floor.

Here, methought (it seemed to be) is the past tense of methinks (it seems to me), but methink and methinking are virtually never used today (if ever).

Methinks

The thinks in methinks means "seems", and traces back to the old English word þyncan, while the more common meaning of think (to cogitate) traces back to þencan. These two words had merged by Middle English.

In Internet slang, sometimes methinks is used simply to mean "I think". I can't find a definitive explanation for this usage, and I opine that it's a combination of (1) a reanalysis of the existing word methinks, since "I think" and "it seems to me" have similar meanings, and (2) the /me command in IRC (Internet Relay Chat).

In IRC, /me is replaced with the user's name, so if one types /me thinks it's getting late, the message that gets sent is D. R. Whispers thinks it's getting late. It's not a big leap away from /me thinks to methinks.

Other interesting words in The Raven

A quick list of other words and phrases I found interesting in the poem:

Tell me what thy lordly name is on the Night’s Plutonian shore!”
            Quoth the Raven “Nevermore.”

Plutonian: from the underworld. Pluto was the Roman god of the dead. And we named a(n ex-)planet and a cartoon dog after him.

 Respite—respite and nepenthe from thy memories of Lenore;
Quaff, oh quaff this kind nepenthe and forget this lost Lenore!”

Nepenthe(s): a drug that makes one forget about grief. From Homer's Odyssey.

“Prophet!” said I, “thing of evil!—prophet still, if bird or devil!—
Whether Tempter sent, or whether tempest tossed thee here ashore

Tempter: the Devil. The Big Bad from Down Under.