The word takes its root from comedic wit, such as puns and comedies of error. For example, in the musical, "A Funny Thing Happened on the Way to the Forum" there is a character who has searched for his missing children for decades. A captain of the army comes to his town to wed a virgin concubine, only to find out that she is actually his sister and they are children of the old man. Furthermore, they were only reunited with their father because another character, seeking to disrupt their marriage for the benefit of his master, pretended to be a fortune teller that would help the old man find his kids and then actually did, inadvertently, through his devious acts. That's ironic. While also unexpected and coincidental, the irony stems from the circumstantial nature of the event.

Rain on your wedding day is not ironic. Holding your wedding in April in Arizona with the theme "April Showers", knowing that it very rarely rains in Arizona in April and thus making light of the point, and then having it rain in the middle of your ceremony...that would be ironic.

From Wikipedia's article on the word, the best description I found was "a contradictory outcome of events as if in mockery of the promise and fitness of things". It is the comedic relief that comes from recognizing the curveballs you are thrown just when you have it all figured out. Often, it's the situations that help the underdog.

Generally speaking, because they are circumstantial, most ironies must be deliberate or else unique to that situation. A "No Smoking" sign on top of a poster of a smoking Sherlock Holmes (seen in the Wikipedia article) is not in of itself ironic. However, someone deliberately placing a no smoking sign atop that poster would be. This photo is ironic because it is unique to the situation: http://bit.ly/6SqBsD

While we're on the conversation, can we please stop using the word "literally" to mean something happened, as in "I literally ate the whole sandwich." That implies that you did not do something figuratively, but there is no figure of speech having to do with eating a sandwich. It is an explanatory word, not an emphasis. "He literally went around the world in 80 days" is an accurate way to describe your friend's 80 day trip across 4 continents. "Did you hear? NASA is building a spaceship that can literally travel faster than the speed of light." Accurate. "I literally worked for 12 hours straight on this"...please revise and resubmit!