A miracle is a supernatural event that violates the known physical laws of the universe.
O.K. just a couple of thoughts on this to kick us off.....
1) I think the adverb "known" is important. If we keep that adverb there (and as I say I'm happy to go by any definition you wish to pick) then miracles definitely exist. One key example I would pick is the creation of the universe, which would appear on face value to violate what we know about thermodynamics. There are no known physical laws of the universe that describe
ex nihilo creation (assuming we accept the scientific "big bang" hypothesis). We can't say in what circumstances
ex nihilo creation occurs, we can't say how it occurs and we can't predict when it will next occur or even if it will occur again. According to our current set of laws "something out of nothing" should not happen. Our knowledge of physical laws simply does not extend to how creation began, or what caused the big bang if you prefer. Some things happen which we just don't understand and
appear to violate our existing laws, though that simply drives scientists to explore what is missing in our current laws which could explain these unexplained events. If they are miracles (and one may call
ex nihilo creation a miracle I think) then miracles exist and I have hopefully given you an acceptable example. Maybe though what appears miraculous today will later be explained.
2) The verb "violates" is also important. If one were to say that a miracle is something that must violate natural/physical laws (now assuming we have a complete set of natural/physical laws) then I think this could be a short discussion, as I will agree with you and say "I don't think they happen". If God is creator of the universe, then that includes creator of how the universe works and I can't see it as an acceptable position to say that God would violate his own natural/physical laws of the universe. For me anything that appears as a miracle must essentially work in harmony with creation and not against it. We may not understand "how" (e.g. how Christ was resurrected) but I would not want to say Christ was resurrected and it violated the physical laws of the universe.
Essentially I believe that ultimately natural (events) and "supernatural" (miracles) are all part of the same creation and the distinction is largely based on the state of our knowledge. The miraculous may become mundane once explained; though ultimately I believe we will see it all as one beautiful harmony and recognise the miraculous in things we today consider mundane.