"Now if Christ is preached as raised from the dead, how can some of you say that there is no resurrection of the dead? But if there is no resurrection of the dead, then Christ has not been raised; if Christ has not been raised, then our preaching is in vain and your faith is in vain. We are even found to be misrepresenting God, because we testified of God that he raised Christ, whom he did not raise if it is true that the dead are not raised. For if the dead are not raised, then Christ has not been raised. If Christ has not been raised, your faith is futile and you are still in your sins. Then those also who have fallen asleep in Christ have perished," (1 Cor. 15:12-18).
Fr. Tim Finigan over at The Hermeneutic of Continuity has an excellent post on the way many have come to treat death these days.
I knew a priest who told me a story once about when his father died. At the burial service, a family friend approached him and asked if he "knew where his father was," to which the priest responded, quite simply, "Yes, he's there in the ground."
In his work Mere Christianity, C.S. Lewis famously said that "we don't have souls. We are souls. We have bodies." This is simply mistaken. We are neither our souls nor our bodies. Angels are souls, "spirits," if you prefer. And rocks are bodies. We are neither. We are humans. Composite beings composed of two principles, one material, one immaterial--a body and a soul. Each is equally important, intimately bound up with the other, and dependent upon it.
At death, our souls are separated from our bodies. This is an unnatural event. It should not occur. Our souls are not designed to exist outside our bodies. The only reason it is possible is due to the grace of God. In a very real sense, then, when we die, that is us there in the ground. Of course, it is also us that goes, God willing, to be in Heaven. This lasting connection is why we mark graves, erect shrines, and venerate relics.
This is why death is both a time to grieve, and a time to take solace in the hope we have in Christ and his Church. Our loved one is dead. His body, his self, has died. Each death we experience throughout our lives is a reminder of our own death to come, and that the days we have been given to "work out [our] own salvation with fear and trembling" grow ever shorter, (Phil. 2:12).
Nevertheless, after death, by the grace of God, our souls continue to exist. More than that, we believe that one day this event will be undone. Our bodies will be resurrected from the ground and reunited with our souls as Christ's was on that Easter morning 2011 years ago (or so).