Limited Atonement: For Whom Did Christ Die?

Did Jesus die for the sins of the whole world, or only the sins of the elect? Did Jesus's death purchase a mere possibility for all, or was it absolutely effective for certain individuals? What does the Bible say? 

For more information, see: 

Canons of Dort, Second Head of Doctrine 

Death of Death in the Death of Christ by John Owen

From Heaven He Came and Sought Her: Definite Atonement in Historical, Biblical, Theological, and Pastoral Perspective by Johnny Gibson 

Redemption Accomplished and Applied by John Murray 

But for the Grace of God: An Exposition of the Canons of Dort by Cornelius Venema