There is one verse that describes a spirit going to heaven when we die:
… and the dust returns to the earth as it was, and the spirit returns to God who gave it. (Ecclesiastes 12:7)
This is an allusion back to Genesis 2:7 and the creation of Adam.
He was made from dust and God breathed into him the “breath of life” to make him a living person. The word “breath” is the same as the word “spirit” in Hebrew. When we die, the life-force that keeps us alive returns to God. He keeps all things alive by his power or spirit. This is not a conscious part of us, it is simply the power of God that keeps us alive. Psalm 104:29-30 says much the same thing about animals.
There is nothing in scripture about us having any kind of consciousness while dead (apart from a few highly allegorical poems in the prophets). In fact, several verses teach quite clearly that there is no consciousness in death. See Ecclesiastes 9:5; Psalm 6:5; 115:17.
The Bible does describe the hope of life after death, but it is on earth and not in heaven, and it happens when Jesus returns, not the moment we die.
See After death what? for more information.

#1 by Kim Green on June 26th, 2010
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who do you think the army of 10s of thousands that come back to earth with Jesus on white horses to fight against satan and his army are?
#2 by Rob J Hyndman on June 27th, 2010
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I assume you are referring to Revelation 19:14 which is the only verse in the Bible that refers to an army on white horses. However, it says nothing about the riders coming “back to earth”. It simply says they are the “armies of heaven”. Most likely, these are angels. Of course, being in Revelation, we should not take the description too literally.