The last comment to my post missed my point that was perhaps unclear.
All the responses have identified great scientists. In this forum, surprise, surprise, most are physicists! I indicated, and it is a view, or opinion, that singular views aligning with limited criteria can not determine the greatest scientist. This will clearly apply across the general population, if you take an informed vote. In my view, no scientific definition is possible of the greatest scientist where it certainly can not be determined only by scientists.
I would ask not only which scientist had the greatest results in their field but who has not only exerted the greatest influence across science and has had the most impact on the world. That includes social impact, philosophical impact, economic impact, political impact, educational impact, and so on. This goes far beyond scientific impact (across all of science) and not just the singular impact within a scientific field.
It is interesting to note that where Darwin is widely considered the greatest biologist of all time, he did not seem to rank as a candidate for greatest scientist of all time in this forum. I would add that Darwin's work extends far beyond what he is renowned for; his early insights on behavior are recognized by neurologists, including, for example, Eric Kandel. These early considerations enable Darwin to place our race alongside the rest of the animal kingdom with no evolutionary separation necessary.
I find this topic interesting because I think that Darwin's activity represents the finest example of the scientific process at work where this is readily comprehensible to the general population. I believe that we have largely lost support for scientific activity where there is little understanding, across the general population, of what science really is about; that is, what science can offer culturally, socially, educationally, philosophically, economically, etc. beyond the singular pursuit of advanced knowledge for its intrinsic value. Scientific progress often follows the form of assimilating broad principles out of diverse inconsistent incomplete information. This sounds quite like the real world where the scientific method seems more and more irrelevant every day, at least to the controlling majority.