I do not believe in curses. Throughout history, folklore surrounding spells, curses and hexes developed as a way to explain what could not be explained, included chance occurrences, coincidences and various happenings. While not everything about our natural world is yet known, our modern level of scientific sophistication can now often find logical and realistic explanations for these events.
Without any real, peer-reviewed scientific evidence to back up claims of a curse, it is impossible, I feel, to believe in such things. Since the dawn of time, Man has constantly been drawn to mystical, ancient relics. Due to the age of such items, fears develop and superstitions come to the fore. However, without proof, you cannot say that curses are real.
I don't believe in anything supernatural, because I can't believe in anything without evidence. I believe in chance, and I think that things, places, people, etc. who are believed to be "cursed" are just experiencing or associated with bad luck of some kind. Unusual things will happen sometimes, just because of chance.
Curses were a theory that made sense in an age without the same level of scientific learning as ours. However, it is easy to see now that there is no evidence to support the existence of curses. If someone experiences bad luck after visiting a cursed place, it is only because they are noticing it more because of confirmation bias.