I've come to realise it's more useful to study flawed clues, so I've started a separate section which takes examples of these from published puzzles and analyses them. This exercise has caused me to rethink some of what I'd written originally below and to make revisions and additions. I hope the article will provide food for thought but don't expect revolutionary insights.

By 'clue' I mean British-style cryptic clue. (There's something to be said for the witty/clever, off-beat definition clues that sometimes appear in US-style puzzles but not in this article.) A good cryptic clue must be properly constructed, of course. By this I mean:
It has a definition and an element of wordplay (or cryptic definition/multiple definition or an & lit construction).
The wordplay element obeys logical rules enabling the solver to work out the solution - e.g. any anagram is properly indicated, it doesn't contain extraneous words unhelpful to the solver, etc.
Definition and word play should not overlap (except in the case of an & lit).
It should read well and make sense as a sentence/phrase.
I recognise it's possible to break one or or more of the above 'rules' yet produce a good enjoyable clue and I'm delighted when this happens. More often than not, though, such liberties seem to have been taken merely for the sake of surface reading - or, worse, to make the setter look clever. Which brings me to the most important 'rule' ...
Above all, the clue should - however ingenious, however devious - be fair to the solver.

So, given the above, what is it that makes some clues special? Well, I'm sure most people would cite wit, succinctness and aptness/topicality. Beyond that there are likely to be differences of opinion - between individuals, of course, but also between categories of crossworders. I'd say there are three main groups, each having its own take on and approach to the crossword: solvers, setters and clue competition entrants. Let's look at clues from the point of view of each of these groups.

1) Crossword setters - as a setter myself I 'appraise' other setters' clues of course. I can be impressed by their clever or humorous clues but I know that such flashes of brilliance often come about by luck. What I really like to see is a clue which, though not great necessarily, has clearly taxed to the full the setter's skills and resources. I would put into that category Fawley's clue for NYMPHET: Nabokov’s refusal to restrict rate of progress for Lolita? (MPH inside NYET). Good clues for words that are difficult to clue or fresh, creative clues for 'old chestnuts' I appreciate too. Certainly, when I as a setter manage to produce the goods for a seemingly 'unclueable' word/phrase, I get the biggest kick of all. One example is the awkward 'CFCs' (refrigerant, etc. gases.) for which I managed:
 They don't improve the atmosphere of Chile’s premier football clubs.

We often praise the brilliant clue but perhaps we'd do ourselves more of a favour as solvers by showing our appreciation for clues where the setter has gone the extra mile to provide a fair and entertaining challenge. We should be encouraging setters to put solvers' best interests first, not to show off with clever, flashy clues (which, I'm afraid, often means they're obliged to 'cheat' when wording the clue).

2) Clue-writing contestants/judges - I'm not all that keen on clue-writing competitions (nothing to do with the fact that I'm not very good at them, of course). Don't you think there's something unsatisfactory, sterile, about a clue isolated from its companions and its crossword grid? Successful clues often don't seem to be judged on whether, in a real crossword context, they'd present solvers with a satisfying challenge. The judges often talk of 'elegance' in clue construction, which I take to mean the clue not only reads well (indeed, rolls off the tongue) but is deftly and succinctly expressed or aptly captures the essence of the solution. In the end, though, I feel that a competition clue, to be successful, needs to have a 'stand-out' quality that begs for it to be taken out of its box, as it were, for closer study and admiration. To be honest, I find such a clue just a bit too pleased with itself!

Nevertheless, competitions do produce some ingenious clues. What's more they illustrate the many ways it's possible to clue the same word - and even when two cluers have adopted the same approach, there's often a surprising difference in their chosen wording.
Here are a couple of good examples, taken from an  About.com competition for a clue for FRANKENSTEIN:
Clue 1 - Open, with intense trembling, a classic tale of shock and horror. (by Gordon Murray)
Clue 2 - Patchwork monster ran, sent knife reeling. (by Patti Itterman)

3) Solvers - the most important group and setters should not forget this! No doubt there are those solvers who want clues that are safely within their capability, so they can feel comfortable - or, within their own limitations - clever. There are also those who delight in obscure words and references, spending many a happy hour riffling through reference books or tapping away at computerised word finders and the like. However, I'm sure the majority of cryptics solvers prefer to be stretched mentally by devious clues to words with which they are, on the whole, familiar. They want something that tests their problem-solving ability rather than their knowledge/memory (though that comes into it). If they can be surprised or made to smile along the way, that's all to the better. For that reason, I think solvers are impressed less by an individual brilliant clue than by the overall effect of all the clues in a puzzle. It's on that basis they'll most likely judge the setter.

Of course, all solvers will stop to admire a setter's ingenuity now and again and, more importantly, take delight in a clue that's exceptionally satisfying to solve, one with the ah! of course! factor. This sort of clue often takes a while to solve; it can be quite frustrating - the solver might even become convinced there's been an error by the setter or a misprint. But when the penny drops finally, the solution is so obvious the solver kicks him/herself for not seeing it immediately! For me this the best sort of clue of all. As a setter, I'd love to know the secret of writing such a clue but, alas, I think it's most likely to come about almost by accident - I'd probably not even recognise it as such until later. There is one celebrated clue, however - I'm ashamed to say I've forgotten by whom - whose author must surely have realised immediately that he'd hit the jackpot.
The clue is simply: GSGE (9,4). (In case you want to work it out for yourself, I'll put the solution at the end of this article.) The example clue seems to break virtually all the 'rules' of good cryptic clueing I listed above. It contains neither definition nor cryptic indication (the solver has to supply these) yet I think it's ultimately fair. Its 'breaking of the rules' provokes agreeable surprise and humour - and it undoubtedly has the ah! factor.

Well, as I warned at the start, I don't think I've come up with any ground-breaking revelations about the essence of a good cryptic clue. I've enjoyed setting down my thoughts, though, and hope those of you who are still with me have found something of interest and perhaps at least one new angle on the subject.