Christ on the Cross (1627), by Francisco de Zurbarán (1598-1664) [public domain / Wikimedia Commons]
[Important Note: I have now, upon reflection, decided that many of the passages below are weak arguments (see my thoughts on that in the related paper, Dialogue: Does the Bible Teach Limited Atonement?). Therefore, I have removed it from listings of papers on my blog. My revised position is explained in the referenced and linked paper]
Luke 19:10 (RSV) For the Son of man came to seek and to save the lost. (cf. “sinners”: Matt 9:13; Mk 2:17; Lk 5:32; 1 Tim 1:15)
John 1:29 The next day he saw Jesus coming toward him, and said, “Behold, the Lamb of God, who takes away the sin of the world!
John 3:16-17 For God so loved the world that he gave his only Son, that whoever believes in him should not perish but have eternal life.  For God sent the Son into the world, not to condemn the world, but that the world might be saved through him.
John 4:42 They said to the woman, “It is no longer because of your words that we believe, for we have heard for ourselves, and we know that this is indeed the Savior of the world.”
John 6:33 For the bread of God is that which comes down from heaven, and gives life to the world.
John 6:51 I am the living bread which came down from heaven; if any one eats of this bread, he will live for ever; and the bread which I shall give for the life of the world is my flesh.
John 8:12 Again Jesus spoke to them, saying, “I am the light of the world; he who follows me will not walk in darkness, but will have the light of life.”
John 9:5 As long as I am in the world, I am the light of the world.
John 12:31-33 “Now is the judgment of this world, now shall the ruler of this world be cast out;  and I, when I am lifted up from the earth, will draw all men to myself.”  He said this to show by what death he was to die.
John 12:46-47 I have come as light into the world, that whoever believes in me may not remain in darkness.  If any one hears my sayings and does not keep them, I do not judge him; for I did not come to judge the world but to save the world.
John 17:21 that they may all be one; even as thou, Father, art in me, and I in thee, that they also may be in us, so that the world may believe that thou hast sent me. (cf. 17:23)
Acts 3:26 God, having raised up his servant, sent him to you first, to bless you in turning every one of you from your wickedness.
Acts 17:30-31 The times of ignorance God overlooked, but now he commands all men everywhere to repent,  because he has fixed a day on which he will judge the world in righteousness by a man whom he has appointed, and of this he has given assurance to all men by raising him from the dead.”Romans 5:18 Then as one man’s trespass led to condemnation for all men, so one man’s act of righteousness leads to acquittal and life for all men.
Romans 11:13-15 Now I am speaking to you Gentiles. Inasmuch then as I am an apostle to the Gentiles, I magnify my ministry  in order to make my fellow Jews jealous, and thus save some of them.  For if their rejection means the reconciliation of the world, what will their acceptance mean but life from the dead?
Romans 11:32 For God has consigned all men to disobedience, that he may have mercy upon all.
2 Corinthians 5:14-15, 19 For the love of Christ controls us, because we are convinced that one has died for all; therefore all have died.  And he died for all, that those who live might live no longer for themselves but for him who for their sake died and was raised.. . .  that is, in Christ God was reconciling the world to himself, not counting their trespasses against them, and entrusting to us the message of reconciliation.
Ephesians 3:8-9 To me, though I am the very least of all the saints, this grace was given, to preach to the Gentiles the unsearchable riches of Christ,  and to make all men see what is the plan of the mystery hidden for ages in God who created all things;
Colossians 1:19-20 For in him all the fulness of God was pleased to dwell,  and through him to reconcile to himself all things, whether on earth or in heaven, making peace by the blood of his cross.
1 Timothy 2:3-6 This is good, and it is acceptable in the sight of God our Savior,  who desires all men to be saved and to come to the knowledge of the truth. For there is one God, and there is one mediator between God and men, the man Christ Jesus,  who gave himself as a ransom for all, the testimony to which was borne at the proper time.
1 Timothy 4:10 For to this end we toil and strive, because we have our hope set on the living God, who is the Savior of all men, especially of those who believe.
Titus 2:11 For the grace of God has appeared for the salvation of all men,
Hebrews 2:9 But we see Jesus, who for a little while was made lower than the angels, crowned with glory and honor because of the suffering of death, so that by the grace of God he might taste death for every one.
2 Peter 2:1, 15 But false prophets also arose among the people, just as there will be false teachers among you, who will secretly bring in destructive heresies, even denying the Master who bought them, bringing upon themselves swift destruction.. . .  Forsaking the right way they have gone astray . . .
[If these are people who never were saved (as a Calvinist would say), then how can it be stated that Jesus “bought them”? Believers in Limited Atonement think that Jesus only “buys” those who are indeed saved and of the elect]
1 John 4:14 And we have seen and testify that the Father has sent his Son as the Savior of the world.