Heaven/Hell-going at death is logically incompatible with the Biblically revealed Divine scheme.
The typical Christian view, if I am not mistaken, is that one has an immortal soul which does not cease to exist at the end of one's life, but rather goes to either heaven or hell, depending on the faith of the individual.
I believe this idea is logically incompatible with the Bible's clearly illustrated promise of bodily resurrection.
The scheme is, briefly, as follows: one lives one's life and dies, returning to the "dust of the earth" (cp. Gen.3:19); at the appointed time, Jesus Christ will return to the earth; the first thing he will do, is raise "many of them that sleep in the dust of the earth" (Dan.12:2); following this resurrection, there will be a judgement seat, in which "they that have done good" will be given "everlasting life", and "they that have done evil" will be 'condemned' (see Jn.5:29).
Commonly, Christianity slots "going to heaven/hell" in between dying and being resurrected (correct me if I am wrong). They say the following: one lives one's life and dies, and one's body returns to the "dust of the earth", whilst one's immortal soul goes to heaven or hell, depending on the individual's faith; Christ returns at the appointed time and raises the dead, an operation in which the 'souls' take on their bodies again (ie. the bodies are resurrected). I am somewhat unclear as to what they believe happens after this.
But what is the point in resurrection if one already has one's reward in heaven or hell? Paul clearly states in 1Cor.15:13-14, that our faith is worthless, indeed, we would have no hope at all if there was no resurrection. If, then, our hope is to go to heaven, why a resurrection?
Some more points for discussion, namely, the faithful men and women in the Bible relied solely on the resurrection for life after death; for a hope of salvation:
Abraham was promised the land of Canaan. "For all the land which thou seest, to thee will I give it, and to thy seed for ever." - Gen.13:15
Yet, Abraham has not yet received this promise, proving that he must be resurrected from the dead (see Heb.11:13,39-40).
Job believed that "the grave" was a place of non-existence, yet he believed in a resurrection (read Job.14:1-14 and compare Job.19:26).
David believed that "death" was a state in which there was "no remembrance of God" (Psa.6:5), yet he was promised that he would see one of his descendants (Jesus - Lk.1:32) physically reign on his throne "for ever" (2Sam.7:12-16). He is told that this kingdom would be established after he "slept with his fathers" in the grave (v12), but that it would also be established "before him" (v16). This clearly implies a resurrection. I know this promise initially applies to Solomon, but it also applies to Christ.
Jesus Christ himself believed that a resurrection was the only hope he had when he died (Psa.16:10; Acts 2:27). Side issue: what happened to Jesus' soul whilst he was dead for three days?
The apostle Paul clearly believed that the resurrection was the only "hope" of salvation from death (Acts.23:6; 1Cor.15; Phillipians.3:11)
Peter's hope was also in the resurrection (Acts.4:2; 1Pet.1:3; 3:21)
Just one more quote to spark some discussion, which I believe strengthens my point:
" And no man hath ascended up to heaven, but he that came down from heaven, even the Son of man which is in heaven." - Jn.3:13
And there's heaps more, but I think I've made my point. The Bible teaches that the resurrection is the only hope of life after death, therefore the doctrine that one's soul goes to heaven after death is incorrect.