Both my wife and I prefer to have our corpses cremated.  When we die, we will be done with our bodies, so why should they take up precious land that could be better used for a park bench or a parking space?  Two generations from now, who will care where we are buried?
 
In the past, Christians favored burial, not cremation, for several reasons:
 
(1) In Jewish culture in both Biblical times and still today, respectful treatment of dead bodies means burial, not cremation.  In the Old Testament, a body that was burned up or was left exposed to be eaten by wild animals was a sign of God's judgment. 
 
(2) Christians look forward to our bodily resurrection with Christ.  Christian burial was viewed as an expression of faith in the resurrection.  People got cremated to mock God and to reject the Bible's teaching about the resurrection.
 
(3) Christians viewed cremation as a pagan practice.
 
However, the Bible does not directly discuss the subject of cremation.  The Bible calls our physical bodies a "tent" which we shed when we go to be with Christ (see 2 Corinthians 4 and 5).  There is practically no difference between turning our bodies to ash in a moment and allowing our bodies to slowly decompose back into the elements of earth.  Christ will not need to find all the pieces of our skeletons nor will He need to hunt up a pile of lost molecules so He can reconstruct our bodies for our resurrection.  The Bible says that He has something much better planned for us(see 1 Corinthians 15).
 
This question about cremation vs. burial has more to do with culture than the Bible.  Cultural attitudes have changed so that now respectful treatment of a body may include cremation, and cremation does not deny our faith in the bodily resurrection that Christ has planned for us.  He promised, "Because I live, you also will live." (John 14.19).