We all know irony is "the use of words expressing something other than their literal intention". However, it is probably misused more than any other rhetorical term.
In another thread I posted a quote attributed to Churchhill, which was "I am reminded of the professor who, in his declining hours, was asked by his devoted pupils for his final counsel. He replied, 'Verify your quotations.'" Since it isn't known if Churchhill actually said this, it can't be verified, and most people I know would consider this "ironic".
There is also the Alanis Morissette song Ironic, where nothing in the song is actually irony. Something like "It’s like rain on your wedding day", isn't really anything, it just sucks. The man afraid to fly who finally takes a flight which crashes isn't ironic, it is just a fluke of chance. This meaning is described by dictionary.com as "used of events and circumstances that might better be described as simply 'coincidental' or 'improbable'." Those words don't really fit too well. My closest attempt would be "cruelly conincidental", although cruelty isn't necessary.
The ancient uses of the term included both verbal irony -- saying one thing intending it to be taken with an opposite meaning -- and dramatic irony, where a character interprets a situation one way ("Kill my father? I'd better leave Corinth to avoid that.") and the audience takes it another way because of their wider knowledge: in ancient drama of course the audience already knew the story.
Many modern uses are a vague form of situational irony, which can be regarded as a derivative form of dramatic irony in which the gods or fates are the knowing audience watching our human drama: we do things with one intention, but the immortals know it will turn out differently.
It has been suggested that the irony of 'Ironic' is not the individual lyrics, but the fact that the song isn't about irony at all. I like that theory as it's about fabulously subtle and intelligent humour, so I choose to believe it .
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