I mean in terms of their whole career, not the work they’re doing currently. If you can’t pick one, feel free to give me a top three.
Without criteria for what you mean by “greatest”, I’m not sure how well this can be answered.
I’d likely go with the obvious choice of Hawking, if for no other reason (and there are plenty of other reasons) than giving us common-folk a glimmer of understanding.
There are many other choices, Feynman and Feshbach (although recently deceased) come to my mind, but IANAP, so the insiders likely will come along and let you know what the thinking is within the discipline. They will also likely have much different criteria than I when making their selections.
I nominate Frink.
I deliberately left the questions of “greatest” somewhat open ended. I guess I could say “Who has made the most significant contributions to our understanding of physics?” Or, perhaps, “Whose contributions would be least likely to be duplicated by someone else, had that person never been born?” I’ve heard the latter definition used in making the argument that Einstein was the greatest physicst of all time – the person making that claim felt that Einstein’s theories so drastically departed from our previous understanding of the universe that it might have been decades before any one else had those ideas. (Of course you could make a strong case for Einstein as “greatest physicist ever” using almost any definition – perhaps his only real competition for the title is Isaac Newton.)
I didn’t really have contributions to the understanding of physics by “common-folk” in mind when I asked the question. While Hawking is a very successful physicist, and probably the most famous physicist in the world to day, I think his fame is due in part to his illness, as well as the fact that he is quite a skilled self-promoter. I’m not trying to denigrate him – the length of time he has survived with ALS is astonishing, and he has made important contributions to physics as well. But I would think that the greatest living physicist would have to at least be a Nobel prize winner (or else someone whose contributions are so great that a Nobel prize is inevitable), which Hawking is not.
20 years ago, I think it would have been Feynman. Actually, Dirac might have still been alive 20 years ago (he died in '84), in which case maybe it was him. But 19 years ago, I’d probably say Feynman.
Hans Bethe is still alive, isn’t he? He probably deserves consideration.
Pi is exactly three! 
Hmm, now that I think about it, I’m thinking the Hawking answer is justified from a “Who has or will have the most impact on physics of the currently living physicists?” perspective.
Much like Tiger Woods is primarily responsible for a huge number of people deciding to learn golf, I think Hawkings has likely had the same impact on physics. I wouldn’t rule out the possibility that the next generation of physicists is full of people who would not have become interested in it if not for him.
Once again, it’s a lot harder to know what the insiders think when sitting out in the stands, so take everything I say with a large dose of salt. While a fan, I will always remain an outsider.
Edward Witten.
In his book The Elegant Universe, Brian Greene made the same statement.
My advisor (Michael Dine, theoretical physicist at UCSC) considers Witten the greatest living physicist as well.
I’m willing to take his word for it.
Of course, Greene is a string theorist, and I take that a good bit of Dine’s research is in string theory as well. I wonder, do people in other areas of physics hold Witten in as high regard? (I’m not saying they don’t – I genuinely don’t know.)
I agree, but unlike Greene, I wouldn’t identify Dine primarily as a “string theorist.” Dine’s most recent papers are on supersymmetry breaking, as far as I know. His name also comes up in cosmology a lot, so I think his work spans several sub-fields of physics.
Good question–I don’t know.
It wouldn’t surprise me if physicists came up with different answers to this question depending on what their area of focus is. 
I will get torn apart for this but I would say thermodynamics greatest living physicist would be Fermi. Fermi, however, is in no way the greatest physicist living as we speak. I think the greatest physicists of any time would be dwelling in theotrical physics just a tad bit.
(I tried to make sense)
Well, it’s always good to try to make sense, but I don’t think you succeeded – at least not to me.
If Enrico Fermi were still alive, he would have my vote as greatest living physicist.
Fermi died in 1954.
I was just trying to say that someone who knows everything about modern physics and has done nothing to further the understanding of physics will never be half as important as the man who does everything to expand physics even if he does not have a huge grasp on modern physics. As in, a physics professor who doesn’t do research is not half as great as the professor who does theoretical physics. Er… I am still not making sense I am afraid. In one sentence: the world’s greatest living physicist has to have a lot of concrete theories to his name. Who is disputing this fact, I do not know, but I just felt an interjection of my guidelines would be fun.
Now, on Fermi, I have no idea what I was talking about. Of course he isn’t alive! Didn’t he win the nobel prize in the '30s and wasn’t he one of the finders of beta radiation? Sorry for two random posts. My mind is running faster than the wheel it’s in!
Also, my vote is with Whitten as well.
That sounds like a reasonable criterion to me.
I’ll chuck Alan Guth, Steven Weinberg and Murray Gell Mann into the mix, although Hawking is a strong challenger even disregarding his heroic efforts to work in spite of his condition.
I don’t know the answer to this, but I know Witten is respected like few other physicists by the mathematical community. He won the Fields Medal is 1990.
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I got 89 Google hits on “greatest living physicist” but only five for “greatest living chemist”. Why all the competitiveness and hierarchy amongst physicists?
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Well, I think a lot of those are historical references, like “the greatest living physicist in 1920 was Albert Einstein.” In fact, I think a lot of the reason that number is so great is that there was once a definite consesus as to the identity of the greatest living physicist. Whereas perhaps there never was as much consensus for chemistry.
Try eliminating results containing Einstein’s name.
If you google: “greatest living physicist” -Einstein
you get only 24 hits.
It drops to 13 if you also eliminate Hawking, which is odd because he is not even a consensus choice for the greatest living physicist right now. But I suppose he is by far the most famous physicist living in the world today.