For starters, please read a fairly balanced short review about Limited vs. Unlimited Atonement with respective biblical support (http://en.wikipedia.org/wiki/Limited_atonement).

Personally, I believe Christ died for all mankind, not just the saved or elect. In addition to the clear bible passages that affirm this view, I have other good reasons to believe so.

First, the death of Christ symbolizes not just sacrificial love and penal substitution, but also God's unflinching judgment of sin. All of mankind, past and present and future, without exception, is declared guilty before God and representatively punished to death on that Friday when Christ was crucified. Did Jesus die on behalf of everyone in this representative and symbolic sense? Yes, He surely did.

Second, the death of Christ for everyone makes those who receive Him all the more humbled and grateful, while making others who reject him all the more culpable and inexorable. If Christ has never even intended to die for the children of perdition, then how can God hold them accountable for rejecting the salvation of Christ? On the day of final judgment, Christ not only will judge the unrepentant sinners for their own wayward wickedness, but also for their stiff-necked, hell-bound unbelief. Unbelief is among the greatest of sins, it is tantamount to blasphemy. Did Christ die for the ungoldy in this sense? Yes, He definitely did, and the righteous Judge shall reckon with those who dare to reject the only savior of mankind.

Third, did everyone participate in the death of Christ? Yes! All of mankind, past and present and future, indeed participated in the crucifixion of Christ. In this light, Christ died because of everyone's rebellion. Christ died for (read: on account of) our sins.

In sum, Christ died for everyone, his death is a redemption for those who repent, and a pronouncement of d-a-m-n-ation for those who reject.