Zakat is required to be paid if a person is:

1) Adult ( have reached the age of puberty)
2) Muslim (Zakat is not paid by non-Muslims)
3) Sane
4) In complete ownership of the Nisab
There are differences of opinion as to whether pre-pubescent children, orphans or the psychologically inept (i.e. insane) should pay Zakat.

See Paying Zakat - Is it obligatory? for further information