Typically, Calvinists are said to be the ones who limit the atonement. But, when you really stop to think about it, every biblical Christian believes in some form of limited atonement. Otherwise, such a person would be a universalist (one who believes that the whole human race will be saved).
So, who limits the atonement - the sinner or God? This really is the crux of the controversy. And on this point the great Baptist preacher Charles Spurgeon set forth a cogent case for the "Calvinist" view:
We are often told that we limit the atonement of Christ, because we say that Christ has not made a satisfaction for all men, or all men would be saved. Now, our reply to this is, that, on the other hand, our opponents limit it; we do not. The Arminians say, Christ died for all men. Ask them what they mean by it. Did Christ die so as to secure the salvation of all men? They say, "No, certainly not." We ask them the next question - Did Christ die so as to secure the salvation of any man in particular? They answer, "No." They are obliged to admit this, if they are consistent. They say, "No, Christ has died that any man may be saved if" - and then follow certain conditions of salvation. Now, who is it that limits the death of Christ? Why, you. You say that Christ did not die so as infallibly to secure the salvation of anybody. We beg your pardon, when you say we limit Christ's death; we say, "No, my dear sir, it is you that do it." We say that Christ so died that he infallibly secured the salvation of a multitude that no man can number, who through Christ's death not only may be saved, but are saved and cannot by any possibility run the hazard of being anything but saved. You are welcome to your atonement; you may keep it. We will never renounce ours for the sake of it.- Cited by J. I. Packer, "Introductory Essay," in John Owen, The Death of Death in the Death of Christ (n.p., n.d.; reprint, London: Banner of Truth, 1959), 14.
Years ago while attending a small Bible Conference at which James Montgomery Boice was the keynote speaker, I asked him about his views regarding the doctrine of limited atonement. I'll never forget his answer: "I believe that when Jesus said, 'It is finished,' He made salvation complete, not just possible."
That's food for thought.