Irony is a much-misunderstood form of humour. It is somewhat culture-specific, being more prevalent where wordplay is common (notably in the UK, where the pun has been raised to an art form), so many people fail to 'get' irony, while others apply the term incorrectly. It is a technique beloved of satirists, and one which is hard to master (there is always the danger of slipping into overt sarcasm which is, as has been observed, the lowest form of wit).
What Irony Is
Imagine that an England cricket captain covertly bets his shirt on the Aussies winning the next test series. He does his best to lose but the England team pull off a historic and completely unexpected series victory. The England captain is left victorious but destitute. That, dear Researcher, is irony.
Irony is defined as...
The humorous (or mildly sarcastic) use of words to imply something different from, and often opposite to, their literal meaning.
An expression marked by a deliberate contrast between apparent and intended meaning, usually to draw attention to some incongruity1 or irrationality.
A literary style employing such contrasts for humorous or rhetorical effect.
Incongruity between what might be expected and what actually occurs, or an occurrence or circumstance notable for such incongruity.
Dramatic irony is a special case where the irony is understood by the audience but not by the characters in the book or play. Socratic irony2 is the process whereby a questioner feigns ignorance in order to lead another to expose their own ignorance.
These types of irony give the clue to the true definition of an ironic statement. An ironic statement must appear as if you are sincere, there must be no hint of sarcasm, and you must not be self-consciously droll. The line must be delivered straight, so that the recipient misses the hidden message but onlookers get it loud and clear. The saying 'Irony is wasted on the stupid' works well as long as the person addressed believes themself to be a sage despite making an absolute ass of themself, and nods wisely in assent.
Thus Fowler's Modern English Usage defines irony as...
... a form of utterance that postulates a double audience, consisting of one party that hearing shall hear and shall not understand, and another party that, when more is meant than meets the ear, is aware of that more and of the outsider's incomprehension.
An ironic statement might be, 'I enjoy avant-garde music - chords are so passé.' Note, though, that this could equally be taken as either sarcastic or hopelessly pretentious depending on the tone in which it is delivered, and the audience. So irony lies somewhere on a line with plain old-fashioned humour at one end, and outright sarcasm at the other.
One often-quoted example of an ironic situation is Joseph Heller's Catch-22. In chapter five of the classic novel, Yossarian and Doc Deneeka discuss the possibility of being grounded due to insanity (thus escaping the appallingly dangerous combat duty). The catch was, you could only be grounded if you were mad, you had to ask to be grounded, and anyone who asked to be grounded clearly wasn't mad any more.
Irony can also be unconscious. It is unlikely that George W Bush was being intentionally ironic when he said that he would not recognise the result of the Zimbabwean presidential election, since the process had been 'flawed'.
What Irony Is Not
Irony can be humorous, but most humour is not ironic. Some informative examples of what irony is not come, ironically, from the Alanis Morissette song 'Ironic'. Here are a few.
An old man turned 98/He won the lottery and died the next day - Tragedy, not irony.
It's a black fly in your chardonnay - Bummer but not ironic (although there is arguably some irony in the fly being black, however this does at least mean you don't ingest it with the drink).
It's a death row pardon two minutes too late - Not irony, just another example of why the death penalty is fatally flawed.
It's like rain on your wedding day - Not even close, unless you've gone from Manchester to Hawaii for your wedding and get the first rain in August for 30 years, while Manchester experiences glorious sunshine, and how likely is that?
A traffic jam when you're already late - certainly fails the 'unexpected' criterion.
A no-smoking sign on your cigarette break - more of a life-saver than an irony, that.
It's like 10,000 spoons when all you need is a knife - Not unless you are in the Acme Knife Factory being approached by a mad axeman and reach behind you for a weapon, only to find that you're in the newly-opened spoon department.
You might find some more irony at The Ironic Times.
Another source of ironic humour is The Onion.
Irony, along with other linguistic phenomena, is discussed in the Radio 4 programme, The Routes of English.