Did the importance of the resurrection increase as the New Testament was written? I've often heard that if you lay out the books of the New Testament by the chronological order of their composition, the story of Jesus' resurrection becomes more important in the later books. Some also say it becomes more supernatural.

Is there any truth to this? I do not know the order of the books by when they were written.
Allow me the liberty to rephrase your question:

Did the concept of Resurrection develop over time?

Yes.  

The ancient Hebrews did not seem to have any conception of life after death.  In Job and the Psalms, we start seeing hints that Israelites envisioned some existence after death, but not as anything very exciting.  If you've read any Homer or the Gilgamesh epic, you'll remember that the dead go to a shadowy, dry place.  But it's important to understand that, unlike the Greek concept of Hades, Sheol wasn't a place where souls existed, but where whatever was left of the dead's body and spirit was housed.  It's not clear that the writers of the earlier books in the Old Testament envisioned anything more than a grave when they used the word.

By the Second Temple period, Jews began to develop more sophisticated cosmologies.  We start getting hints of bodily Resurrection:


  Daniel 12:2 (ESV)
  2 And many of those who sleep in the dust of the earth shall awake, some to everlasting life, and some to shame and everlasting contempt.


But even then, it's not clear if the Biblical prophets (outside of Daniel) were envisioning people actually rising from the dead.  Ezekiel 37 (the dry bones passage), for instance, was probably a statement of hope for the restoration of the nation of Israel.

Jewish writings in the time between the Old and New Testaments show even more development of the idea of Resurrection, which always had strong nationalistic and (during times of occupation) revolutionary overtones.  But the idea was that at some point in the future, God would gather up all of His people and restore them to life all at once.  Nobody would have pictured one man rising from his grave as the (or even a) Resurrection.  Certainly the Messiah would not participate in the Resurrection, except to make way for it to happen, since he wouldn't die.

When we get to the time of Jesus, we suddenly see the Christian conception of Resurrection appear on the scene.  It draws strongly from the inter-testament ideas, but in a fairly radically altered format because the Messiah Himself dies, is buried, and resurrected.  Sometime later, the general Resurrection as envisioned by late, Second Temple Jews was predicted&mdash;along with the return of the Messiah to complete His work on earth.

How did the concept of Resurrection develop in the New Testament?

Surprisingly little.

Our earliest church documents are Paul's letters to various primitive churches.  While it does seem that Paul warms to the subject over the course of his ministry, he does not alter his theology.  In Galatians 2, Paul lets us know that his theology was shared with the leaders of the Jerusalem church (James the bother of Jesus, Peter, and John).  His dispute with them was not whether the Resurrection of Jesus occurred or what it meant, but whether or not it replaced the Mosaic Covenant. 

In First Corinthians (ca. 53-54 AD), Paul gives us one of the earliest formulations of the Christian view of Resurrection:


  1 Corinthians 15:3-8 (ESV)
  3 For I delivered to you as of first importance what I also received: that Christ died for our sins in accordance with the Scriptures, 4 that he was buried, that he was raised on the third day in accordance with the Scriptures, 5 and that he appeared to Cephas, then to the twelve. 6 Then he appeared to more than five hundred brothers at one time, most of whom are still alive, though some have fallen asleep. 7 Then he appeared to James, then to all the apostles. 8 Last of all, as to one untimely born, he appeared also to me.


Many scholars think this represents an even earlier tradition that might have been a creedal statement.  Paul goes on to affirm that there will be a general Resurrection in the future:


  1 Corinthians 15:21-22 (ESV)
  21 For as by a man came death, by a man has come also the resurrection of the dead. 22 For as in Adam all die, so also in Christ shall all be made alive.


This is also the text (remember it's one of the earliest, written 20 or so years from Jesus' crucifixion) that asserts the Resurrection to be critical to the Christian faith:


  1 Corinthians 15:17-19 (ESV)
  17 And if Christ has not been raised, your faith is futile and you are still in your sins. 18 Then those also who have fallen asleep in Christ have perished. 19 If in Christ we have hope in this life only, we are of all people most to be pitied.


If anything, the Gospels, which were written later, downplay the Resurrection by giving us more details about Jesus' earthly ministry.  Mark even ends immediately after the women's discovery of the empty tomb and doesn't provide a post-Resurrection account.  (Whether this was by design or was a historical accident is not known.)



Reference: I draw most of my information from N. T. Wright's The Resurrection of the Son of God, which stands alone as the best survey of the history of the idea of the Resurrection ever written.  If I don't stop now, I'm in danger of summarizing his entire book.