But, are there ways to see if "prayer works" if we stay out of the realm of theology? The Mozambique approach is one that does, because it tests a common form of prayer. Dr. Novella claims that it is bad scientific method to test subjects who know they are being prayed for, but that form of prayer is a common, everyday form. Believers pray for each other with each other. Another common form of prayer is to pray for a person not present but who knows that she or he is being prayed for. If science is prevented from studying these forms of prayer because of methodological considerations, then we have a clear indication that science is ill-equipped to study prayer—not that "prayer doesn't work."
Let's reject the idea that science is unable to study prayer in its various forms including one-on-one prayer. In that case, an interesting approach would be to study a group that prays for other people and for specific outcomes and see how frequently those outcomes actually take place. The goal is not to test whether or not a deity answers prayer. It is simply to see if prayer in some way or another allows us to manipulate our world. From a non-theistic point of view, science may eventually discover entirely naturalistic explanations for the conclusion that under certain circumstances "prayer works" in a measurable number of times.
There are a couple of limitations involved. First, scientists will have to try to discover the impact of their own observations on the prayer process. How does the presence of an observer skew the results? Perhaps, they will have to "blind" the research subjects not from each other but from the observer, but that raises ethical questions about using people for research purposes without their consent. Second, researchers cannot definitively say that prayer doesn't work in all cases or under all circumstances because they can't test all cases and circumstances. Theists can always account for science's failure to find positive test results for prayer, as I indicated above—using explanations science can't test. Science could theoretically affirm that prayer does work (sometimes under some conditions), but it cannot theoretically affirm that it does not work. The best it can do is to say that the scientific study of prayer finds no data proving that it works.
The point is that actually studying the phenomenon of prayer itself is complex and does not admit to simplistic conclusions, not if it is studied as it is actually practiced.