Azkaban

"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."

Azkaban is a wizarding prison located on an island in the middle of the North Sea. Presumably, this prison is only used by magical Britain, as there are other wizarding prisons elsewhere such as Nurmengard. Using certain charms, the prison is hidden from the muggle world, and is unplottable. It is widely regarded as a horrible place, given that its guards, Dementors, cause great suffering to those in their proximity. Most prisoners eventually go insane, and slowly die away.