An A-OK (a okay) is both a saying, derived from okay, and a hand-gesture done by connecting the thumb and forefinger in to a circle (the 'O') and holding the other fingers straight or relaxed in the air.
While the gesture is positive in some countries, in certain parts of middle and southern Europe (although not in Spain or Portugal) the gesture is considered offensive, as in "you are a zero" or "you are nothing". In some Mediterranean countries, as well as in Brazil, it represents vulgar expressions: either an insult ("you are an asshole"), or the slang for anus itself. By the same symbolism, it stands for marica (faggot) in several South American countries.
In Australia it simply means "okay".
In Germany it can either mean "okay" or "arsehole". The latter is mainly used by traffic participants, called the Autofahrergruß (drivers' salutation). Insulting police with this gesture can result in a fee of up to €750
In American Sign Language it is the letter 'F', or the number '9', and when made with the thumb and forefinger parallel to the ground, means "asshole".
In Turkey and Venezuela, it is a very offensive gesture, regarded as a reference to homosexuality, and reflecting a wider than usual (due to anal sex) anus of a homosexual man. In Peru too, but it's upside-down with the middle, ring and pinky fingers pointing down.
In most continental European countries, when the sign is placed over the nose, with the nose protruding through the 'O' made by the thumb and forefinger, it means "drunk".
In Japan it also means "zero" or "money".
In Finland it also used to celebrate the ending of the national service. During their final day in the Finnish Defence Forces, conscripts use it denote they have zero mornings left in their service and that they will receive an honorable discharge during the course of that day. It also used to tease and taunt other conscripts that still have various amounts of "mornings" left and are stuck while their comrades are allowed to leave. Colloquially it is referred to as the "TJ0" or "Tänään jäljellä 0 aamua.", which translates to "Zero mornings left today." The official TJ counter can be viewed on the Finnish Defence Forces website