Is it spelled well thought-out, or well-thought out, or well thought out?
It depends on how you use it... if it's preceding the word it modifies, then it should be hyphenated:
He paused for a bit, and then gave a well-thought-out answer.
However, if it follows the word it modifies, no hyphenation is necessary:
He paused for a bit, wanting to make sure his answer was well thought out.
(My source: Chicago Manual of Style, 14th Edition, sections 6.38–6.40)
I agree with Hellion: when it appears before the noun attributively, it is almost certainly 'well-thought-out', with two hyphens (e.g. a well-thought-out plan). When it follows a noun, it is open (as in, the plan was well thought out).
I take it as noncontroversial that it is open after a noun, so in what follows I'll be discussing the case where it appears before a noun.
The Merriam-Webster dictionary now has an entry for 'well-thought-out', with two hyphens, here. It gives the following example: a well-thought-out plan.
Harrap's Essential English Dictionary has it with two hyphens, as in The play had a well-though-out and original plot. See here.
Google books hits are all over the place, with all combinations appearing (well-thought-out, well-thought out, well thought-out, well thought out). It would be difficult to tally the numbers of hits for each variation, and even more difficult to assign appropriate weights that would reflect how authoritative the source is.
As far as CMOS, it does not treat this case explicitly. But there is no rule that would say it shouldn't have two hyphens (contrary to what some people here have asserted), and what rules there are suggest that both hyphens are appropriate.
Let me first deal with the suggestion that there is a rule that says it should be completely open, with no hyphens at all. That appears on p. 3 of CMOS's summary table, under the category 'adverb not ending in ly + participle or adjective', and it says, 'When the adverb rather than the compound as a whole is modified by another adverb, the entire expression is open.'
Note that for this rule to apply, there need to be two adverbs. Indeed, this is the example given in the table: a very much needed addition. Despite the fact that CMOS puts a hyphen in a much-needed addition, when we add the adverb very all hyphens disappear because the adverb very modifies the adverb much. (On the other hand, CMOS says it is a very well-read child, because here very modifies the whole compund well-read rather than just the adverb well.)
However, in well-thought-out plan there is only one adverb: well. Indeed, thought-out is an adjective (see e.g. here), and thought itself is a participle; nothing in that can count as an adverb. Thus the rule about two adverbs doesn't apply.
Another objection that someone may have (though no one on this page has had as of yet) is that two hyphens simply looks awkward and so CMOS is probably not sanctioning it on that account. But that is not true: CMOS does sanction multiple hyphens in constructions such as a five-year-old child and a fifty-five-year-old woman, both examples appearing at the very beginning of the summary table mentioned above. The table contains many other examples: black-and-white print, a tête-à-tête approach, a one-and-a-half-inch hem (four hyphens!), time-clock-punching employees, an over-the-counter drug, a matter-of-fact reply, an up-to-date solution, stick-in-the-mud, jack-of-all-trades, a mid-eighteenth-century poet...
Now on to 'positive' evidence from CMOS in favor of two hyphens.
First of all, according to the summary table, in the category 'participle + up, out, and similar adverbs' (e.g. dressed-up children, burned-out buildings), it says 'adjective form hyphenated before but not after a noun'. This means it's 'thought-out', just as e.g. Merriam-Webster has it.
Next, when well is added, we are in the category 'adverb not ending in ly + participle or adjective' of the summary table—the same category we considered above. As we saw, thought-out is an adjective, and so the relevant rule is:
Hyphenated before but not after a noun; compounds with more, most, less, least, and very usually open unless ambiguity threatens. When the adverb rather than the compound as a whole is modified by another adverb, the entire expression is open.
We have already discussed why the last sentence does not apply. Thus, it would seem that the rule says that well and thought-out should be hyphenated. After all, well is an adverb (but not one of more, most, less, least, or very) whereas thought-out an adjective, so it's just like the following examples from CMOS: a much-needed addition, a very well-read child, little-understood rules, a too-easy answer, the best-known author. the highest-ranking officer, the worst-paid job, a lesser-paid colleague.
That would be "well thought-out". See http://www.merriam-webster.com/dictionary/thought-out. Adding "well" before "thought-out" does not require a hyphen because well is an adverb.
Whether preceding or following a noun, the phrase is open per Chicago MOS 7.85, "When the adverb rather than the compound as a whole is modified by another adverb, the entire expression is open." Chicago's example: "a very much needed addition."
Therefore, in both constructions, "His plan was well thought out" and "It was a well thought out plan" the phrase would remain open.