I believe the Scientific Method is, if not becoming irrelevant, at least losing its prominence in discourse throughout the world. As anything in the history of the world, this is just a cyclical movement, but I think we're about to witness an inflection point.
Biased by the local version of history, we forget that the Scientific Method is only one possible paradigm of reasoning, one that particularly suited humans who found themselves in the Age of Invention and Exploration. When the number of phenomena being discovered is large and each strengthens the fundamental theories put in place, the Scientific Method feels adequate.
The Scientific Method is -- my amateur definition follows -- the process of rejecting theories through observed contradictory experimental evidence. Synonymous with modern science, it can't prove anything about the world we live in. It can only evaluate theories for how bad they are.
People tend to forget that even the Ancient Greeks -- our model of scientific thought -- believed in reasoning that is a combination of the supernatural (mythos) and the rational (logos). For a long time, we have overemphasized the latter, dismissing alternative approaches to understanding reality, but as science turns strange and more distant, I believe we will begin looking for a basis of our understanding that isn't rooted strictly in observation and rejection of theories.
Science is turning strange. To see this, let's go back to 1905. The world was a fundamentally different place. All motion in the Universe was governed by a few simple rules first formulated by Newton. Mathematicians believed that every statement about the world can be proven or disproven (shown to be false, of course). We just learned to fly. We built automobiles and submarines, harnessed electricity, and were beginning to understand radioactivity. Maxwell unified our understanding of most of physics into an elegant set of equations.
Today, our laws -- even the simple laws of motion -- are more complicated. Sure, at low speeds they reduce to Newton's beautiful equations, but this nonlinearity doesn't give us much confidence that there is no third-order consequence, and beyond, that we're simply yet unable to detect. Perhaps the rules that govern how the universe works are unknowable. Moreover, universe is already known to be unpredictable, in addition to being possibly inscrutable. Particles are in a number of states at the same time. The more we refine our models following observations which refute our hypotheses, the more science begins to look like, well, magic. And while we don't readily admit it, I (and I am sure you, too) feel disappointed by it.
Science is also turning more distant. Many of the advances in physics don't concern us beyond the drama of popular science narrative. It's unlikely we'll directly benefit from the discovery of the Higgs particle, but even if we eventually do (after all, DVDs wouldn't be possible without Einstein, and his revelations seemed "unpractical" enough), we are adding layers of indirection between our theories and our lives.
Instead of focusing on observations, we can listen to our intuition (what feels right?), our sense of beauty (what is elegant?), or even simply focus more on fundamental phenomena and reason about what is not easily unobservable (what is entropy, exactly? What could the underlying cause of the Universe increasing in complexity be?). Doing this would not necessarily be equivalent to a rejection of logic -- I simply advocate for us to go back to the axioms that we base our knowledge base on and revisit them. Once we settle on our axioms, we should absolutely use logic to deduce truths about the world. But that first step is crucial in defining what kind of truths we will discover.
Why would the rejection of the Scientific Method be good for us? For one, it may actually teach us something about the universe. Instead of tweaking existing theories, which are increasing in complexity and losing their elegance, we may be able to think outside the box: take an alternative approach, rethink everything we know about the universe, and settle on a much more intuitive and legible understanding.