Here's the problem that I see: this passage of Scripture is used all too often to preach a mystical Gospel...one in which physical matters fade away while spiritual concerns are elevated. Heaven is seen as a mystical union between spirit beings (us) and God. Almost every thinker/theologian/commentator I read on this passage turned it into something of this nature. And I think that's a big problem. Christians believe in a fleshy (not fleshly) Messiah. We believe in an incarnate God, who walked among us, who put on flesh and bone. We believe in a God who created matter and relationships, for His glory. We believe in a God who created marriage "because it is not good for a man to be alone"--and this was before sin was brought about in the world! Furthermore, we believe in a Jesus who said of marriage, "what God has joined together, let not man separate." If God forbids us to destroy the oneness of marriage, which He has created, then why would He destroy this union? Sure, there are dicey issues to figure out, like what about somebody like Elisabeth Elliot who married 3 wonderful Christian men (she was widowed twice)? But maybe that's the point of Jesus' story: heaven is much more than we can imagine. And marriage may well look different in heaven than it does on earth. But the relationships we build on earth do not just float away. Being in the kingdom of God is so thoroughly relational, and it is brought to fullness and completeness through the koinonia or fellowship we have with other Christians.
The bigger picture here is not to toss out a view of heaven which includes a restored creation, a restored earth. Romans 8 tells us, "We know that the whole creation has been groaning as in the pains of childbirth right up to the present time. Not only so, but we ourselves, who have the firstfruits of the Spirit, groan inwardly as we wait eagerly for our adoption as sons, the redemption of our bodies" (NIV). Note those key words: creation and our bodies. This is talking about something very physical and real. We see that from I Corinthians 15 that the body we will be given will be different from those on earth, like a seed is planted to grow into something more majestic. Who knows, maybe we will be able to stick our hand through people! But the relationality and the fulfillment of all that God intended in His creation of the Garden of Eden seems to me to be certain. In 2 Peter 3, we see that all that is will be destroyed, but then there will be redemption and re-creation, "in keeping with his promise we are looking forward to a new heaven and a new earth, the home of righteousness" (NIV). Heaven is a place where "'the dwelling of God is with men, and he will live with them. They will be his people, and God himself will be their God. He will wipe every tear from their eyes. There will be no more death or mourning or crying or pain, for the old order of things has passed away" (Revelation 21:3-4, NIV). And so, we are exhorted that when our loved ones who are believers die, we are not to "grieve like the rest of men, who have no hope. We believe that Jesus died and rose again and so we believe that God will bring with Jesus [at the Second Coming] those who have fallen asleep in him" (I Thessalonians 4:13b-14, NIV). Here we see that part of Jesus' Second Coming includes the restoration of relationship.
The picture of heaven that I hold to is that heaven is God's new creation. He has already given us the New Adam (in Jesus Christ), and He will yet give us the New Garden of Eden, where relationship and life are restored to be as He originally planned them to be--and maybe even better! If marriage and our other relationships look different in heaven than they do on earth, we need to trust that those relationships will be better than they were on earth! We will not be random spirit beings floating around, but relational beings, in unhindered relationship with God and each other. There will be a wholeness to our relationship. Heaven will be like a big party with your family, but without sin. It is being together in relationships, with God at the absolute center of it all.