From the name of 90's pop songstress Alanis Morissette, referring to her 1996 hit single "Ironic" in which a number of circumstances that were not classically ironic were famously referred to as such many times across many media for several months.
Rain on a day on which one would prefer it did not rain, as, for instance, one's wedding day.
Getting stuck in traffic when you're already late for work.
Meeting the man of your dreams, and then finding out that somebody else liked him enough to marry him.
Licking a flag pole in winter and getting your tongue stuck to it.
Throwing rocks at a bear, and then getting mauled by said bear.
Having relations with a prostitute and, as a result, contracting a venerial disease.