I have heard many people ask and now I have been considering the question myself. Will there be sex on the new Earth? What is the reasoning for either position?
There is very little Biblical evidence to suggest that there will be no sex on the new Earth nor in Heaven after Christ's second coming.
The idea spawns from an inferred interpretation of Mark 12:25
When the dead rise, they will neither marry nor be given in marriage; they will be like the angels in heaven.
The background story is that the Pharisees are attempting to trap Jesus and pose the question of who a woman would be married to after the resurrection if she has been widowed seven times. Jesus replies that she will be married to none of them.
What Jesus did not say is that there will be no sex or no procreation.
This idea is very old and comes from a time when it was unthinkable sin to copulate outside of marriage. Sex and marriage were so intertwined at times in some Christian cultures (Puritan) that they were equated. Some thought, and I am sure that some actually still do, that because there is no marriage then there surely is no sex either.
Without this verse, the Bible is silent on this issue.
Today, I do not know of a single denomination that teaches that there will be no sex after the Resurrection, though I would not be surprise if there are a few small groups, and I reserve the right to be corrected.
Another inference about this scripture is that there will be no gender in Heaven. That is clearly related, but takes the idea to the next level. I discuss this in the answer to a different question.