I think the consensus is self-evident: it is by far the most common method of randomization used in analog games. The D6 is ubiquitous. Designer after designer demonstrably settles on the D6. I don't think anyone has done or will do a scientific study of the prevalence of the D6 over, say the D12, but I think it is pretty obvious.
Some in this thread have asserted that the D6's ubiquity is simply because they are readily available, making them cheaper and more convenient. That might well be a factor, but begs the question of why D6s have built and maintained such popularity. Why wasn't it always the dodecahedron, or whatever, that caught on?
1. D6s seem to provide a good amount of randomization: enough to create options, not too many to manage. You can do a lot with a D6, and rolling multiple D6s can expand the numerical range while keep the math fairly simple. But a whole lot of games work well with 1-6 options.
2. It's a basic, intuitively easy to grasp geometrical shape. Kids basically start with three shapes: circle, triangle, and square. Fashioning circles and triangles into 3d randomizers is problematic (spheres because obviously and pyramids seem to give too few options and don't roll well...plus they're lethal if you step on them!), leaving us with the cube. It's Platonically ideal. They roll just enough to be pleasing, but not so much that they roll forever. Playing craps with D12s would be a pain in the butt.
Game designers have a zillion options but keep coming back to the D6. It works.