Is there a word for when an action has an effect opposite to the one intended?

A common idiom expressing this concept is "to backfire". For example:

• The campaign to reduce smoking backfired.

It's called a Paradoxical Reaction. In general terms, I think you call something like that a paradox.

I believe this may also be considered irony; specifically situational irony.

Such situations could therefore be described as ironic, but probably only upon second reference, when the facts of the matter had already been established.

e.g.:

First mention: The headache-treating drug was known to have caused headaches.

Second mention: Dr. Stephens reported the drug's ironic effect to the FDA.

I just found this term recently and thought that it will be useful for somebody:

The Streisand effect is the phenomenon whereby an attempt to hide or remove a piece of information has the unintended consequence of publicizing the information more widely, usually facilitated by the Internet.

[Wikipedia]

This term is now specific to mass media / Internet, but it will be possibly penetrating in the other relevant fields. However, general concept here is a bit more specific here: forbidding something can possibly rise an interest in something and thus cause a more wide spread (i.e. an opposite effect of intended action).