Christianity has never envisioned an ethereal, wispy eternity where we exist simply as souls forever. The historic Christian view has always been that God will one day raise our bodies from the dead. For example, the Apostles Creed, accepted by all branches of Christianity for over fifteen-hundred years, states, "I believe . . . in the resurrection of the body." As John Piper discusses in the two-minute audio supplement in the link above, heaven is a precious reality but the resurrection of our bodies into the new heavens and new earth is our ultimate hope as Christians.
The Church's belief in this doctrine (called "glorification") is squarely rooted in Scripture. Speaking of Christians, Paul states that "the dead will be raised imperishable" (1 Corinthians 15:52) and that "God has not only raised the Lord, but will also raise us up through His power" (1 Corinthians 6:14). Jesus often spoke of the coming resurrection of the dead (Matthew 22:30-31; Luke 14:14; John 11:25), and taught that "an hour is coming, in which all who are in the tombs will . . . come forth; those who did the good deeds to a resurrection of life, those who committed the evil deeds to a resurrection of judgment" (John 5:28-29).
This truth is so important that the Scriptures teach that we are to fix our hope not first and foremost upon the fact that we go to heaven when we die, but rather upon the fact that God will raise us from the dead to be with Christ forever in our bodies. Paul alludes to this in Romans 8:23 where he states that we are "waiting eagerly for our adoption as sons, the redemption of our body" (Romans 8:23).
This also seems to be what Paul is getting at in 2 Corinthians 5:1-9 when he states that while he would prefer to be "absent from the body and to be at home with the Lord" in heaven to this present life, he longs even more for the day when our bodies will be raised because "we do not want to be unclothed [i.e., without our bodies in the intermediate state] but to be clothed [i.e., with Christ in our resurrected bodies], so that what is mortal may be swallowed up by life" (v. 4). As Piper states, "This means that the great final hope of the Christian is not to die and be freed from our bodies, but to be raised with new, glorious bodies" (John Piper, "What Happens When You Die").
Perhaps most clear on this point is 1 Thessalonians 4:15-18:
For this we say to you by the word of the Lord, that we who are alive and remain until the coming of the Lord, will not precede those who have fallen asleep. For the Lord Himself will descend from heaven with a shout, with the voice of the archangel and with the trumpet of God, and the dead in Christ will rise first. Then we who are alive and remain will be caught up together with them in the clouds to meet the Lord in the air, and so we shall always be with the Lord. Therefore comfort one another with these words.
What is noteworthy is that Paul did not command us to comfort one another with the truth that Christians who have died are in heaven--although that is very true and precious. Rather, he commanded us to comfort one another with the truth that God will one day raise up those who have died to be with the Lord forever spiritually and physically.
That is where our main hope lies, and that is where we should draw our primary strength in the face of death. Death is an enemy that God intends to fully conquer and fully destroy, and that is only accomplished by raising His people from the dead: "When this perishable will have put on the imperishable, and this mortal will have put on immortality, then will come about the saying that is written, `Death is swallowed up in victory. O death, where is your victory? O death, where is your sting'" (1 Cor. 15:54-55). Notice from this passage that it is when the resurrection occurs, and only then, that death is fully swallowed up in victory. As John Murray has expressed it,
The redemption which Christ has secured for his people is redemption not only from sin but also from all its penalties. Death is the wages of sin and the death of believers does not deliver them from death. The last enemy, death, has not yet been destroyed; it has not yet been swallowed up in victory. Hence glorification has in view the destruction of death itself. (Redemption: Accomplished and Applied, 175).
Therefore when we ponder and encounter the reality of death, our confidence and hope lies in the knowledge that death does not have the last word--it will be fully undone.
John Murray, Redemption: Accomplished and Applied, "Glorification"
Wayne Grudem, Systematic Theology, chapter 42, "Glorification"
John Piper, Future Grace, part IX, "The Finality of Future Grace"