There are several types of irony.
Socratic irony - When someone pretends to be naive about a certain subject, and uses his questions about it to point out a flaw in the established belief. This is often used on the TV show South Park, where the children often ask questions about a situation until the folly in a parent's decision becomes clear.
Sarcasm - Understatement, mocking overstatement, or heavy-handed irony (stating the flat opposite of the truth) where both parties are aware of the difference between what's said and what's actually happening.
Situational Irony - The irony that most people think of. A difference between what you expect to happen (in a story, for example) and what actually happens. Rain on your wedding day would be a sort-of example, because a wedding day is generally expected to be a perfect, happy day. The good advice you didn't take, however, would NOT be irony, because that has nothing to do with what is expected and what isn't expected. A traffic jam when you're already late wouldn't be irony either; there's no automatic expectation that traffic will be fine, just because you happen to be late.
Irony of Fate - The concept that the Gods, Fates, etc. are toying with humans for amusement by using irony. Beethoven's loss of hearing is a famous example; one would expect a composer to be able to hear his compositions, but fate denied him that ability.
Tragic (Dramatic) Irony - When the audience knows something that some of the characters don't know in a play/movie/novel/whatever. For example, when the horror flick psycho is in the house and the homeowner just goes in without suspecting anything.
Guy 2: Yeah he was totally awesome and against capitalism and shit which is so cool an im like him.
Guy 1: ....and you dont see the conflict, the irony, in wearing a t-shirt produced by a huge corperation dead set on money making that has the face of one of the most famous communist revolutionaries to date on it?
Guy 2: Dude what?