Mathematics. Just think of a world without it. And reconsider.
A close runner-up for me is the World Wide Web, as it provides for a new dimension in which people (and digital objects) can connect, both for science and otherwise. Of course, this somewhat includes the invention of computers and the Internet as well as, further back, transistors, clocks and the concepts of numerals (especially zero) and alphabets.
Next are the Big Bang theory and the Darwinian theory of evolution by natural selection, which sets the framework for understanding the universe and the living world.
Then come the telescope and microscope, since they were the first means by which humans became able to experience spatial scales that differ from our usual sensory experiences.
From there, it is not far to Magnetic Resonance Imaging and Spectroscopy – a set of techniques that uses quantum mechanical properties of matter to non-invasively deliver images (or chemical information, or both) of internal structures from many different kinds of objects, including living beings, and possibly as small as single cells.
In my research, I am trying to combine Magnetic Resonance Imaging (preferably at microscopic resolution) with evolutionary theory and some subfields of mathematics (especially topology), making intensive use of the World Wide Web. The closer I come to realize this combination, the more it feels like approaching a Big Bang.
The laser. It was invented purely for research, there were no known uses at the time so it was purely science to extend knowledge. Nothing else. Since then it’s been used for loads of things so it’s a great example of why we do science.