Limited Atonement
This seems to be the biggest stumbling block to those who resist the teachings of Calvinism. Many people think that in order for God to be "fair" -- naturally, they are looking at fairness from a human perspective -- Christ must have died for every single person. After all, John 3:16 says, "For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life." And, of course, there's 1st John 2:2: "He is the propitiation for our sins, and not for ours only but also for the sins of the whole world."
When it comes to limited (or, more accurately, particular or definite) atonement, God's word is quite clear on the subject. In Matthew 20:28 and Mark 10:45 we read that Christ gave his life as a "ransom for many." In John 10:11-15 Jesus talks about laying down his life "for the sheep." Contrast that with Matthew 25:32-33, where we see the shepherd separating "the sheep from the goats."
Jesus continues with this analogy in John 10:24-27:
So the Jews gathered around him and said to him, "How long will you keep us in suspense? If you are the Christ, tell us plainly." Jesus answered them, "I told you, and you do not believe. The works that I do in my Father's name bear witness about me, but you do not believe because you are not part of my flock. My sheep hear my voice, and I know them, and they follow me."
Still, we cannot get around the fact that the Bible does teach that Jesus did, in a sense, lay down his life for the world. The answer, as usual, lies in the context.
Paul writes in 1st Timothy 4:10 that Christ is "the savior of all people, especially of those who believe." Now, we know that he isn't the "savior of all people" in the same sense that he is the savior of the elect. If that were the case, then all people would be saved, and given the context of what scripture has to say about the eternal judgment of the wicked, we know that can't be what Paul meant. Rather, Christ is the savior of all people in that by saving some, humanity itself has been saved from complete destruction.

Another way to look at limited atonement is to consider what the term "propitiation" means in 1st John 2:2. It means to satisfy God's demands. God demands perfection, something sinful man can never hope to achieve. Jesus Christ, however, lived a perfect life and suffered our punishment on the cross, thereby satisfying God's holy justice. Our debt has been paid. To assume that Christ also paid the debt of those who ultimately end up in hell is to make God out to be unjust as one who punishes the same sins twice.
If we are to be honest, we will agree that both Calvinists and Arminians limit Christ's atonement in some way. Did Jesus die for Satan and his demons? Certainly not. The atonement is at least limited to human beings. Do all people eventually end up in heaven? Again, no. There is no disputing the fact that the effects of the atonement do not extend to all people in the same way.
Here is where we differ: Arminians limit the effectiveness of the atonement in that they believe it merely made salvation possible for sinners. Since they deny the Calvinist view of total depravity, unconditional election, and irresistible grace, they are forced to admit that there is the theoretical possibility that not one person would ever "accept Christ as savior." After all, if they wish to remain consistent in holding to the concept of "free will," then they must deny that God would give certain people the extra grace needed that would enable us to do what scripture says we cannot do on our own (Romans 7:18).
Calvinists, on the other hand, limit the scope of Christ's atonement rather than its effectiveness. We would agree with Arminians that his death on the cross was sufficient to cover the sins of all. There certainly would not have been a need to have his suffering increased accordingly in order to cover the sins of each and every person. But that isn't how the atonement was designed. We believe that the atonement accomplished exactly what it was supposed to do by actually securing the salvation of all those for whom it was intended (i.e., the elect). "For by a single offering he has perfected for all time those who are being sanctified" (Hebrews 10:14).
To say that God intended to save everyone, but, despite his best intentions, was unable to accomplish that goal, is to make God into something less than the sovereign, all-powerful Creator that he is. How much more God-glorifying it is to say, without hesitation or qualification, that he did
exactly what he set out to do!
Part 1: Total Depravity
Part 2: Unconditional Election
Part 3: Limited Atonement
Part 4: Irresistable Grace
Part 5: Perseverance of the Saints