The misuse of ironic is a common peeve among careful users of English. Some of the complaints are overblown, but ironic has undoubtedly been overextended.
The one definition of ironic of which everyone approves is using words to express the opposite of their literal meaning. Irony is similar to sarcasm, but the goal of sarcasm is to mock, while irony is usually used to make subtler points.
The following writers use ironic in its one unassailable sense:
And yes, I do say ‘LOL’ out loud. In almost an ironic sense, like a slow handclap after a bad joke. [quoted in BBC]
Is the publicly-funded body being ironic by epitomising in one document the very thing that it says it is against? [Financial Times]
“The Free World,” with its darkly ironic title, takes these lives deeper; they are treated with more respect, but no less love, than they were in “Natasha.” [Los Angeles Times]
A less accepted but longstanding definition of ironic is markedly different from what was expected. This is where ironic starts to rankle some people. But while this sense of ironic is more questionable than the original, it’s so widespread that we have to accept it. It’s even common in edited writing—for example:
It’s sad and ironic that wranglings over abortion should in any way impede action that could save babies’ lives. [Guardian]
There’s something ironic, in a limited sense, in the man’s moving to the suburbs and hurting himself on his own lawn. [Children’s Literature, Seth Lehrer]
It may seem ironic that workers in a nominally Communist country don’t have the right to strike. [New York Times]
While today’s English speakers have no choice but to accept ironic as a synonym of paradoxical, incongruous, or contradictory, the word is overextended where it becomes a synonym of funny, interesting, improbable, appropriate, or coincidental. For example, there are more fitting words than ironic in each of these instances:
Stefano sang “End of the Road” by Boys to Men, an ironic choice [a fitting choice?] considering he’s been close to the end of the road on this show for weeks. [Fox News]
I find it ironic [appropriate?] that the Chicago Flubs, er, I mean, Cubs are playing their home opener on April Fool’s Day. [Chicago Tribune]
It is somewhat ironic [interesting?] therefore, that Col. Gadhafi is under NATO and U.N. attack while Mr. Mugabe continues to terrorize Zimbabwe unhindered. [Washington Times]