Vanishment

Vanishment is the art of vanishing objects i.e., causing object to cease to exist. It is one of the four branches of Transfiguration, and is the opposite of Conjuration (another branch), which brings objects into existence.

Nature
Compared to the other three branches, Vanishment appears moderately difficult - it is taught in Fourth Year at Hogwarts School of Witchcraft and Wizardry and up - and is considered one of the hardest transfigurations to be tested on in one's O.W.L. The difficulty of the Vanishment to be performed positively correlates with the complexity of the organism to be Vanished. For example, invertebrates are easier to Vanish than vertebrates, whilst mammals are more difficult.

Methods
There are several methods one can employ to Vanish an object, described below.

Vanishing Spells
Unlike conjuring spells, Vanishing spells all follow the same, simple incantation - Evanesco, Latin for "disappear". The intent of the caster directs the spell, Vanishing the target.

The Vanishing Cabinet
The Vanishing Cabinet is a special piece of furniture in Hogwarts School of Witchcraft and Wizardry that randomly Vanishes & reappears. As such, it be used to Vanish things for a variable but finite length of time (since the cabinet always reappears at some point in the future).

The Room of Requirement
Like the Vanishing Cabinet, the Room of Requirement also appears and reappears, though in accordance with one's wishes. Things left in the Room after one no longer has need of it will be Vanished along with the Room itself until a later date (when one has need of that specific object, at which point it will be conjured up inside the Room for them to retrieve).

Behind the scenes

 * Vanishing sickness is a wizarding illness treated at St. Mungo's Hospital for Magical Maladies and Injuries. It is unknown if Vanishing is the cause or effect of this illness though it appears to be related to the contraction of some sort of magical bug (since it is treated in the "Magical Bugs" section of St. Mungo's).
 * According to W.O.M.B.A.T., it may be possible to Vanish both inanimate and animate objects.
 * It is unknown if the Vanishment of a living creature would result in said creature's death, or merely send it into a conscious, intermediate state until it is naturally Conjured back into existence. According to Minerva McGonagall, Vanished objects enter "everything", possibly suggesting that Vanished entities do have some form of existence, albeit an unknown kind.
 * It may be possible to retrieve Vanished objects, as Bill Weasley possibly Vanished some of the Order of the Phoenix's plans in order to hide them (though it is also possible that he used a teleportation spell).

Appearances

 * Harry Potter and the Chamber of Secrets
 * Harry Potter and the Goblet of Fire
 * Harry Potter and the Order of the Phoenix
 * Harry Potter and the Half-Blood Prince
 * Harry Potter and the Half-Blood Prince (film)
 * Harry Potter and the Half-Blood Prince (video game)
 * Harry Potter and the Deathly Hallows 
 * Harry Potter and the Deathly Hallows: Part 2
 * Harry Potter and the Deathly Hallows: Part 2 (video game)