Did Christ Die For Everyone?

One of the central tenets of Calvinism is "Limited Atonement" -- that Christ did not die for everyone.  He only died for the elect.  Arminians believe in "Atonement for All" -- Christ died for everyone.  What does the Bible say?  You be the judge.

• John 1:29 The next day John saw Jesus coming toward him and said, “Look, the Lamb of God, who takes away the sin of the world!
• John 4:42 And they told the woman, “We no longer believe because of what you said, since we have heard for ourselves and know that this really is the Savior of the world.”
• 2 Corinthians 5:14-15 For the love of Christ compels us, since we have reached this conclusion, that one died for all, and therefore all died. And he died for all so that those who live should no longer live for themselves, but for the one who died for them and was raised.
• 2 Corinthians 5:19 That is, in Christ, God was reconciling the world to himself, not counting their trespasses against them, and he has committed the message of reconciliation to us.
• 1 Timothy 2:5-6 For there is one God and one mediator between God and mankind, the man Christ Jesus,  who gave himself as a ransom for all, a testimony at the proper time. 
• 1 Timothy 4:10 God, who is the Savior of all people, especially of those who believe.
• Titus 2:11 For the grace of God has appeared, bringing salvation for all people
• Hebrews 2:9 But we do see Jesus—made lower than the angels for a short time so that by God’s grace he might taste death for everyone—crowned with glory and honor because he suffered death.
• 1 Peter 3:18 For Christ also suffered for sins once for all, the righteous for the unrighteous, that he might bring you to God.
• 1 John 2:2 He himself is the atoning sacrifice for our sins, and not only for ours, but also for those of the whole world.
• 1 John 4:14 And we have seen and we testify that the Father has sent his Son as the world’s Savior.

What about Mark 10:45 which says, "For even the Son of Man did not come to be served, but to serve, and to give his life as a ransom for many”?  There are two possible explanations.  First, the word "many" is in contrast to a few, rather than all.  The point is that Christ gave His life for lots of people, not just a few.  The point is not that Christ only died for some.  Second, the author's intent could simply be that while Christ died for everyone, it is only effectual for the many who trust in Christ.  Salvation is extended to all, but only those who trust in Christ are saved.