Why shouldn't Jews be cremated?
There are a number of reasons, but one is that Jewish law mandates that the human body be treated with respect, even after death. This is true for both Jews and non-Jews, since we are all created "in the image of G-d" (Gen. 1:27); for Jews there is the additional idea that the body was in its lifetime a vehicle for mitzvos (the Divine commandments), and so it should be handled respectfully even after it has ceased to serve that function, like a worn-out Torah scroll or similar sacred objects.
Cremation goes against this idea, and is seen as a degradation of the body. We thus find Amos (2:1) excoriating the king of Moab for "burning the bones of the king of Edom into lime."
There's an excellent article summarizing this and many other considerations, at chabad.org.
In addition to the halachic issues invloved there is an emotional aspect to burial vs cremation. There is no place for family to visit, or a memorial. I recently discovered that a great-great-uncle of mine was cremated and I realized that there is nothing remaining of him on this earth. There may be no emotional benefit to burial for the deceased, but there certainly is for the living.
In the near future when Moshaich will hopefully come, all the Jewish souls will be resurrected and reunited with their bodies in Israel. If one has his body cremated after death then he or she will no longer have a body to reconnect with their soul.
I posted about this awhile back here - http://ishimshitos.blogspot.com/2009/08/ashes-to-ashescremation-controversies.html