Some passages I've always found particularly salient in this regard are 2 Peter 3:9 (copied here for ease):
The Lord is not slow in keeping his promise, as some understand slowness. He is patient with you, not wanting anyone to perish, but everyone to come to repentance.
and Ezekiel 18:23 and 33:11, which virtually say the same thing (the latter is copied here):
As surely as I live, declares the Sovereign LORD, I take no pleasure in the death of the wicked, but rather that they turn from their ways and live.
and I Timothy 2:4
God our Savior, who wants all men to be saved and to come to a knowledge of the truth.
What these verses tell me, indisputably, is that God wants people, all people, saved. There is no glory in his mind in anyone being lost. There will not be one person thrown into eternal torment whom the Lord would not rather have by his side in glory. Which leads to another thought-- why can't God have what he wants? I mean he is omnipotent, omniscient, omnipresent and outside time. What stands in the way of such a God getting what he desires? Certainly, if he desires it, it must be good by definition!
As some fashion them, the so-called doctrines of grace declare that people get saved because of a sovereign act of God. He chooses, they believe and persevere, irresistibly. The only thing that stands between heaven and hell is God pushing the grace button within the soul. Once pushed, salvation is inevitable.
Is that a problem? Yes, if we actually take what God has told us about himself to be true! He has said of himself that he doesn't want anyone to be lost. The scripture is clear about this. If all it took to accomplish his desire was his own act, how would he act? Since I'm not willing to diagnose God as schizophrenic (as I would have to in order to say that he has a stated desire, a desire that must be good, but cannot bring himself to use his sovereign power to accomplish it), I must answer that He would save everyone.
Not everyone will be saved, however. There must be some other factor in the equation that God is not willing to circumvent. Suffice it to say, to hold on to sovereign election as promulgated in the doctrines of grace and also to accept God's testimony about himself, one would be forced, it seems to me (and perhaps the history of Calvinistic churches in New England bears this out), to inevitably fall into the trap of adopting universalism.