Science has struggled for many years to study and quantify the existence of the paranormal. By it's very definition, paranormal phenomena are outside the rules we've created for how our universe should work. The scientific method has been very reliable in predicting, discovering, and defining the rules that govern the world around us. From it, technological and medical advances have helped greatly improve our quality of life.
One of the biggest problems facing this kind of research is that it can be difficult to reproduce the same results from one study to another. The scientific method requires that all relevant variables are controlled and measured in order to maintain consistent standards between different studies of the same nature. It can be really hard to reproduce exactly the same conditions, in the same way in a laboratory environment, to produce consistent results.
I like to think of the scientific method as a reliable way to study and quantify the rules that govern the universe around us, as it would exist without sentient life. (quantum mechanical events seem to indicate that the observer is a must to collapse the wave-form of potential events, but the wave-form itself exists without an outside observer) A useful analogy could be to see the universe around us as the bigger dream (a construct created by a higher intelligence) and our own consciousness, as the smaller dream, collapsing the wave-form of potential outcomes, as well as having a measure of influence over them. The rules within the bigger dream form our consensus reality. Our own minds influence this larger consensus reality through the observer effect. This is why I think experiments that utilize large groups of people, focusing on a single point of intention can have more effect on world events than those that focus only on individuals alone (such as the Maharishi Effect). I believe that paranormal phenomena does indeed exist, even if on average it occupies a small part of our daily lives.