If you ask a bunch of people on who is the most influential physicist of, let's say, since the beginning of 1900, you would get the usual answers: Einstein, Feynman, Bohr, Heisenberg, Dirac, etc... all the big names. However, consider this: there is only ONE person who has won the Nobel Prize for Physics twice; this person is a co-inventor of the most important device that is now the foundation of our modern society that we use everyday; and this person is not on that list above.
Ladies and Gentlemen, let me introduce you to John Bardeen!
In my book, John Bardeen is the physicist that has the MOST direct influence on all of our lives. His first Nobel Prize was awarded for the invention of the transistor along with William Shockley and Walter Brattain. To say that the transistor has revolutionized our world would be almost an understatement, unless one has no clue what a transistor is and why it is useful.
That invention alone would have been sufficient to put him at the top of this list, but nooooo.... His second Nobel Prize in Physics pushed him way over the top. He is the "B" in the BCS Theory of Superconductivity, along with Leon Cooper and Robert Shrieffer. The BCS theory is considered to be one of the most successful and highly verified theories in all of physics. Till 1986, it was thought that the BCS theory has explained everything there is to know about all of superconductivity. However, the significance of the BCS theory goes way beyond just explaining a single phenomena. It marked one of the earliest sucesses of the application of quantum field theory in the emerging field that is now known as condensed matter physics. This sparked further refinement of the field theoretic methods in the study of materials, something that we now are reaping the rewards from. So the impact of this theory transcends beyond just what it describes.
But why isn't he more well known?
He is one of those rare breed of physicist that isn't eccentric, is not loud, profoundly understated, and intensely private. While the general public may not even know of his existence, those of us in physics, and especially in condensed matter physics, have nothing but the utmost respect and admiration for him as a person, and his body of work.
I highly recommend the biography of Bardeen written by Lillian Hoddeson, Daitch Vicki, Vicki Daitch titled "True Genius: The Life and Science of John Bardeen" (National Academies Press, 2002). This could be the most fascinating and important person that you have never known.