Ask ten different people what they define as a miracle and you'll likely get ten different answers. So, before I answer, I'm going to define what I mean when I say "miracle."

I found a very informative article on the subject that describes my point of view quite well. Here are a couple of excerpts:

"To satisfy the inquiring mind on the question of miracles requires that the evidence in connection with them point to (1) a superior power, (2) their possibility from a scientific point of view and (3) the reason for or purpose of the miracles. A miracle, amazing to the eye of the beholder, is something beyond his ability to perform or even to understand fully. It is a work requiring greater power or knowledge than he has. But from the viewpoint of the one who is the source of such power it is not a miracle. He understands it and has the ability to do it.

Understanding the miracles of the Bible, then, begins with belief in a deity. If a person believes in a deity, particularly in the God of creation, he cannot consistently deny God’s power to accomplish things awe-inspiring to the eyes of men.—Rom. 1:20.

MIRACLES AND NATURAL LAWS

But how are we to understand the relationship of miracles to natural laws? Well, through study, researchers have noted various uniform operations in natural things, and have recognized laws that govern this uniformity. The Encyclopædia Britannica gives as an example of a “law of nature” the law of gravitation. Scientists admit the complexity and yet the reliability of these laws, and in calling them “laws” imply the existence of One who put such laws into force.

Skeptics who accept such laws view a miracle as a violation of these laws, which they accept, reasonably, as irrevocable, inexorable: therefore, they say, a miracle never occurs. However, it is good to keep in mind that they do not fully understand the operation of these laws. Nevertheless, their attitude is that ‘if it is not understandable and explainable to us as far as we discern these laws, it cannot happen.’

However, capable scientists are becoming increasingly cautious about saying that a certain thing is impossible. Professor John R. Brobeck of the University of Pennsylvania stated:

“A scientist is no longer able to say honestly something is impossible. He can only say that it is improbable. But he may be able to say that something is impossible to explain in terms of our present knowledge. Science cannot say that all properties of matter and all forms of energy are known. . . . [For a miracle] one thing that needs to be added is a source of energy unknown in our biological and physical sciences. In our Scriptures this source of energy is identified as the power of God.”—Time, July 4, 1955.

Since this statement was made, further scientific development has made it more emphatic.

When you stop to think about it, do scientists fully understand the properties of heat, light, atomic and nuclear action, electricity or any of the forms of energy or matter, even under normal conditions? No; and still more deficient is their understanding of these properties under unusual conditions.

For example, only recently have extensive investigations been made under conditions of extreme cold, but in this brief time, many strange actions of the elements have been observed. Lead, which is not an ideal electrical conductor, when immersed in liquid helium cooled to a temperature of -456° Fahrenheit, strangely becomes a superconductor and a powerful electromagnet when a bar magnet is placed near it. At such supercold temperature helium itself appears to defy the law of gravity by creeping up the side of a glass beaker and over the edge, draining itself out of the container.—Matter, Life Science Library, pp. 68, 69."

The article itself continues with the following subheadings:
"No Violation of God's Own Laws," "Contrary to Human Experience?" "Bible Miracles Not Mere Natural Happenings," "Characteristics of Bible Miracles," "Purpose of Miracles," and "A Different Situation Today."

Put super simply and more succinctly, I do believe in miracles. I believe they are things God has done using his superlative understanding of the natural world around us and the physical "laws" he has put into place that we may not, as of yet, fully understand, but that can be explained by science and will be at some point in the history of the world.

If the article interests you at all, email me and I'll cut and paste the rest of it to you.