My favorite form of irony:
When a character in a book does or says something without knowing the future impacts. An excellent example is when Oedipus decrees that king Laius' murder will be executed to run from town. Unfortunately, Oedipus is in fact the ex-king's assassin.
Most of the time when people point out irony, they are unaware that dramatic irony and literal irony are completely different.
As someone pointed out earlier, Bender defines literal irony when he says "The use of words expressing something other than their literal intention. Now that IS irony!". This is in response to Lela's signing over her hand to the Robot devil to get new robotic ears (after being deafened) in order to hear Fry's opera (the final episode of the show). Unfortunately, the contract Lela signed was an agreement to marry the Robot Devil. Technically, as a work of Drama, this could qualify as dramtic irony (the kind most people erroniously point out in real life) as well a literal irony in the context of the show.