Azkaban

Azkaban is the wizarding prison. It is on an island in the North Sea.

Azkaban was guarded by dementors until most of them revolted and joined Lord Voldemort in summer of 1995. Prior to their revolt, the only persons ever to escape the prison were Sirius Black and Barty Crouch Jr. Sirius was able to escape by changing into his dog form; Barty Crouch, Jr. was smuggled out by his father, Barty Crouch Sr. and replaced with his mother using Polyjuice Potion.

There is some type of graveyard outside the wall of Azkaban where the Dementors bury those who die.

known Azkaban convicts
They don't need walls and water to keep the prisoners in, not when they're trapped inside their own heads, incapable of a single cheerful thought. Most go mad within weeks.
 * Antonin Dolohov
 * Augustus Rookwood
 * Barty Crouch, Jr.
 * Bellatrix Lestrange
 * Crabbe Sr.
 * Crispin Cronk
 * Igor Karkaroff
 * Jugson
 * Lucius Malfoy
 * Marvolo Gaunt
 * Morfin Gaunt
 * Mulciber
 * Mundungus Fletcher
 * Nott
 * Percival Dumbledore
 * Rabastan Lestrange
 * Rodolphus Lestrange
 * Rubeus Hagrid
 * Sirius Black
 * Stan Shunpike
 * Sturgis Podmore
 * Walden Macnair
 * Wilkes

Azkaban in the movies
The role of Azkaban in the movies is the same as it is the books, though there appears to be an added scene in The Harry Potter and the Order of the Phoenix film where the 1995 mass breakout at Azkaban is shown. In the film Azkaban appears to be a tall building in the shape on an "A".