Before we can decide whether or not miracles can happen, we must first define what a miracle is. Basically, a miracle is an event that cannot be normally explained through the laws of nature. In the context of Christianity, miracles are the product and the work of God who created the natural laws as well as the universe.
However, vital to the discussion of whether or not miracles can occur is the issue of a person's presuppositions. If someone believes that there is no God and also believes in what is called naturalism - that all things in the universe are subject to natural physical laws - then miracles are defined out of existence. That is, the universe is defined in such a way as to make miracles impossible. Therefore, if someone says that miracles cannot happen, then it is most probable that he denies the existence of God and/or believe in naturalism along with its companion, evolution.
On the other hand, if someone believed that there was a God and that God is involved in the world, then it is easy to acknowledge that miracles can occur. If God created the universe as the Bible states (Gen. 1), why can't God also intervene in our world and perform miracles? Take the resurrection of Jesus, for example. With an atheistic, naturalistic presupposition the resurrection of Christ could not occur since people simply do not rise from the dead, no matter what is said. Therefore, the account of Jesus' resurrection must be wrong. Either the Bible is untrustworthy, the witnesses collaborated on a lie, Jesus never died, He only appeared dead, His body was stolen to make it look like He'd risen, or someone else died in His place. Either way, the non-God, non-miraculous presupposition would not allow the skeptic to believe in the resurrection of Jesus, especially after three days of being in the tomb. It just could not have happened, no matter what. The problem is that with this kind of presupposition, objectivity can be thrown out the window. This is especially ironic since many atheists consider the Christians to be the ones who lack objectivity.
Weigh the Evidence
If someone believed that miracles were possible because he believed that God exists, then all he needs to do is look at the Bible, weigh the evidence and decide to believe or not believe in miracles -- like Jesus' resurrection. Again, consider Jesus. From the accounts of the eyewitness testimonies in the Gospels we can see many people believed that Jesus rose from the dead. After all, the Romans, who were expert at crucifixion, killed Jesus, and put guards on the tomb. Yet, the tomb was found empty. The disciples who had all fled and were in hiding, suddenly started proclaiming that Jesus had risen. These same disciples risked life and limb in order to teach that Jesus had risen. Why would they do that for a lie that would cost them their lives, their livelihood, their family ties, etc., unless it really happened?
Since Christians do not have a presupposition that excludes the miraculous, we are able to look at the resurrection of Christ as recorded in the Bible, weigh the evidence, and make a choice to believe or not believe. Of course, Christians by default believed in the resurrection of Christ.
Finally, it would be basically illogical to state that miracles cannot occur. This is because in order to logically state that miracles cannot occur, a person must either know all things in the universe so that he can rightfully state miracles cannot occur, or he must have some logical proof why miracles cannot occur, or possess a sufficiently sophisticated knowledgebase to conclude the miraculous cannot occur, etc. Furthermore, it is not enough to state that there is no evidence for the miraculous since a person's experiential base is limited. It may very well be that miracles have occurred and this person is simply not aware of it.
Therefore, at best someone could simply say "I do not believe that miracles occur because (insert reason)." At least this leaves open the possibility that they may occur. And if they might indeed occur, why not have the possibility that Jesus who claimed to be God (John 8:58 with Exodus 3:14), who fulfilled Old Testament prophecies (i.e., Psalm 22:11-18; Isaiah 7:14; 9:6, Micah 5:1-2, etc.), who predicted his own death and resurrection (John 2:19-21), appeared to people after his public execution (Luke 24:39; John 20:25-28), did indeed actually rise from the dead? Since the eyewitness accounts have been accurately transmitted to us, would it not be logical to believe the witnesses who described what they saw? It would seem so.
Can miracles occur? Yes, they can because there is a God in the universe.