A questionable site, referenced in the Triads as the prison of Arthur, and in Culhwch ac Olwen.
References
"And I have been in Caer Oeth and Annoeth, and in Caer Nefenhyr; nine supreme sovereigns, handsome men, saw we there, but never did I behold a man of equal dignity with him who is now at the door of the portal." --Glewlwyd Gafaelfawr to King Arthur in Culhwch ac Olwen
"And one (Prisoner), who was more exalted than the three of them, was three nights in prison in Caer Oeth and Anoeth, and three nights imprisoned by Gwen Pendragon, and three nights in an enchanted prison under the Stone of Echymeint. This Exalted Prisoner was Arthur. And it was the same lad who released him from each of these three prisons- Goreu, son of Custennin, his cousin." --The Welsh Triads
"There has been the family of Oeth and Anoeth--
Naked are their men and their youth--
Let him who seeks for them dig in Gwanas." --"The Stanzas of the Graves.
The grave of March, the grave of Gwythur;
The grave of Gwgawn Gleddyvrudd
A mystery to the world, the grave of Arthur. (anoeth bid bet y Arthur")--"The Stanzas of the Graves.
A Problem of Etymology
The word anoeth is used in "The Stanzas of the Graves" as signifying something that is "a wonder" or "difficult." The prefix an- either works as a negator or an intensifier, but which is uncertain. John Rhys in Celtic Folklore defines oeth as "power"
The word oeth--or here oet--appears in the Black Book of Carmarthen in the poem "Arthur and the Porter." Here, the word is translated as both "hard" and "deep"; Rhys gives an interesting example:
Ny bei duv ae dikonhei.
Oet dihed aghev kei.
Unless it were God that wrought it,
Hard to effect were the death of Cai.
Rhys is drawing on the word cyfoeth, which in Middle Welsh meant "power" or "dominion", but now refers to "riches", cyf working as a prefix.
Elsewhere, the poem "The Stanza of the Graves" refers to both the Teulu Oeth ac Anoeth and to Arthur's grave as anoeth. Teulu means household, and the poem states that the graves of the Household of Oeth and Anoeth can be found in Gwanas, a mountainous area around Cader Idris in the Snowdonia range. Anoeth is usually defined as "hard", "difficult" or "a wonder"--with the implications that Arthur's grave is difficult to find (perhaps non-existant) or a wonder. Both definitions seem to work on the idea that an- is an intensifying prefix. Only in Rhys is anoeth defined as "weak."
Speculations
I have seen at least one speculation that the word anoeth was originally Agned, which would mean that Caer Oeth Anoeth and Arthur's imprisonment would refer to the Battle of Mount Agned, identified with Edinburgh. However, I must disagree, as Oeth Anoeth seems to be a purely Otherworldly place.
In The Iolo MSS., we're provided with a story about how after fighting a Roman invasion of Britain, Manawyddan collected the bones of Roman soldiers and created a prison from them; this is then said to be Caer Oeth Anoeth. This, of course, is one of Iolo Morgannwg's inventions.
Finally, in The Prydain Chronicles, it is in Oeth Anoeth that Gwydion is imprisoned, and it is here that he learns the languages of birds.
My own, personal, and entirely conjectural belief is that Caer Oeth Anoeth refers to the Otherworld, but specifically to a land of the Dead. All references to it have some connection to imprisonment or death, and even the word anoeth refers to the conditions of a grave. When Glewlwyd states that he and Arthur have been to Oeth Anoeth, he names it together with Nefenhyr, a word which may have connotations of the sky. Moreover, it (or possibly Nefenhyr, it's unclear) is a land with "nine supreme sovereigns"--which echoes such places as Taliesin's Caer Vedwyd, where "From the breath of nine maidens {the magic cauldron} was gently warmed" or Geoffrey of Monmouth's Isle of Apples, where Morgen and her sisters learn the arcane arts.
If Caer Oeth Anoeth is Arthur's prison, and he is set free by Goreu (the same cousin who slew Ysbaddaden), and it has oblique references to the otherworld, it is likely that--another part of the Otherworld, but one dealing specifically with death.
SOURCES:
Bromwich, Rachel. Trioedd Ynys Prydain. Cardiff: University of Wales Press, 1961.
Hunt, August. "The three Prisons of Arthur" Faces of Arthur Vortigern Studies. URL: http://www.geocities.com/vortigernstudies/articles/guestdan10.htm
Rhys, John. Celtic Folklore: Welsh And Manx. Oxford University Press, 1901.
Skene, W.F. The Four Ancient Books of Wales. Edinburgh: Edmonston and Douglas, 1868. | 
