I'm a Dominican priest, and, yes, I believe in miracles.
Sometimes, people do not accept the possibility of miracles because they think, unfortunately, that miracles are contrary to a scientific account of the world:
In my book, Unlocking Divine Action: Thomas Aquinas and Contemporary Science (Catholic University of America Press, 2012), I try to show that miracles are compatible with empirical science, and that arguments to the contrary are often based not on genuine science, but on the ideology of scientism.
St. Thomas Aquinas defines the word "miracle" in this way:
Note that Aquinas does not say that miracles are "contrary" to [contra] nature, but "outside" or "beyond" [praeter] the workings of nature (and therefore not contrary to, but simply beyond the scientific laws that describe those workings).
For centuries, there has been a remarkable cooperation between scientists and theologians on the question of miracles in the process of the canonization of saints. The process requires authenticated miracles, and the opinion of scientists is essential in that authentication. I once gave a talk on this at a meeting of the Catholic Theological Society of America. For a summary, see Ilia Delio, "Science and the Saint," Catholic Theological Society of America Proceedings 66 (2011): 146-47. Of course there were saints long before there was a canonization process, and devotion to a saint does not always wait on the canonization process. Witness the devotion to José Gregorio Hernández of Venezuela: go to New York Times of 09/30/2014.
Lourdes is known as a place of miracles. When I was there some years ago, however, the most moving miracle (wondrous sign of divine love) I saw was a young man patiently and lovingly calming and comforting his crippled and emotionally disturbed brother during a very long prayer gathering.
In contemplating the reality of miracles, I think we need some humility regarding the limits of our knowledge of the natural world. I'd suggest Shakespeare: "There are more things in Heaven and Earth, Horatio, than are dreamt of in your philosophy" (Hamlet).
And then, we need an openness to wonder and possibilities. For this, I might suggest Rogers and Hammerstein: "A hundred million miracles are happ'ning every day" (Flower Drum Song).