Politics: Wellington, Thatcher (I know she’s not dead yet, but we need people to be in their prime), Macciavelli, Augustus, John Stuart Mill.
Military: Wellington, Julius Caesar, Napoleon.
Religion: Jesus, Mohammed.
Science: Faraday, Aristotle, Euler, da Vinci, Newton.
Music: Handel, Bach, Telemann, Mozart.
Leonardo da Vinci
Michelangelo Buonarroti
Salvador Dali
John Lennon
Hieronymus Bosch
Frank Zappa
Jimi Hendrix
Tristan Tzara
Marcel Duchamp
Diogenes of Sinope
The first 9 I would clone/reanimate because of their artistic genius, and in some cases, the wide scope of their genius. I would clone Diogenes mainly because he’d be fun to have around.
If I could choose more, I would choose Mahatma Gandhi, Leif Eiriksson, Martin Luther King Jr., Lin Chi, Thomas Jefferson, Henry David Thoreau, Albert Einstein, Benjamin Franklin, George Washington, King Harald Fairhair, the historical Odin (if there was one), and Olafur Thors.
Hmmm, and maybe Abraham Lincoln, Woodrow Wilson, and Genghis Khan.
I’d clone Adolf Hitler a bunch of times and spread the clones across the United States, then hide in Brazil.
With my tongue slightly in my cheek on ocassion, but when serious for what the could contribute to the (well MY) pleasure of living in the modern world NOT for their past lifetime achievements:
I’m not seeing how bringing military leaders back from the dead is going to do anything. Or are you going to supply them with an army, teach them what we have learned above and beyond them, teach them how to think modern, use modern weapons and such, then expect them to actually outperform our military leaders of this day? What makes you think they are smarter than our leaders today?
Circumstance is 99.9% of greatness.
I’m not sure how a bunch of hitlers in America is going to really cause any problems. A few people thrown in prison for murder perhaps? You think they will magically garner followers and start murdering Jews again? How many people would follow him in this day and age?
Hey, guys why no comics? Boy, do we need a laugh in the time we live in or what?
On reflection I’ll swap Jesus for Spike Milligan.
Hmm, what are the chances of my ever typing that sentence if I wasn’t a SDoper? 
Epimetheus, unless I’m very mistaken, Captain Amazing was making a reference to the plot of the movie The Boys from Brazil.
I agree with the tenor of these remarks (and yes, I second Marley23’s interpretation of Capt Amazing’s statement), i.e. that circumstances are a large part of how great one can be. This removes a lot of the names that people mentioned. And why anyone would want to bring back tyrants like Genghis Khan is beyond me.
I’ve just noticed that the OP wanted reasons for our picks. Essentially, I’ve brought back leaders who as themselves would make a difference to modern society. I’ve brought back science types who would make a difference even if they had different names.
Here’s my list again:
Golda Meir - I hope she can do something to bring peace to the Israeli-Palestinian situation. The problem there now isn’t the Palestinians, who’ve almost all accepted that the state of Israel is here to stay and just want to live in peace. A change is needed in Israeli government policy - bringing back Meir (or Begin) who’d soon see that things had changed in the past fifty years, and have the stature to change things, would help. After World War Two, Israeli leaders wanted to create a society with a ‘new Jew’, who would never be walked over again. They sure succeeded. But the pendulum never stops in the center on its first swing.
Konrad Adenauer - One of the founders of the European Community, he helped facilitate the West German economic miracle. Before that he was mayor of Cologne, and turned its fortunes around. Europe needs a technocrat-politician leader like him more than ever. Not D’estang!
Malcolm X The black American community (I’m not going to say African American) needs leaders who are smart, principled, not power hungry (unlike say, Farrakhan), who believe in the power of the individual. A leader who could tell black kids not to beat up the black kids who do well in school, and be listened to. A leader who could say, `Look, we’re not one great big homogenous block. We’ve produced folks like Jimi Hendrix, Miles Davis, Danielle Allen, Arthur Ashe and Sidney Poitier. Why this chip on our shoulder?’
Scientists: This is where progress comes from. Tesla, Turing, von Neumann and Newton all shared this in common - they were exceptionally intelligent, did many things and most importantly, tinkered.
Marley23, I don’t see why Newton’s dabblings in alchemy are a problem. I view it as a plus. We only know he was on the wrong track because of hindsight. And yes, he wasn’t just a scientist - he was in charge of the Royal Mint and did a good job of it, e.g. introducing the ridges on the sides of coins (still here today) as a successful measure against counterfeiters.
I thought hard about Feynman, but I don’t think we’d get much more mileage out of him. Faraday is an interesting possibility.
Mathematicians: Easy - Karl Gauss. Erdos and Ramanujan I’ve omitted, as they liked math too much for its own sake. Gauss was more cynical. Poincare is another contender though.
Inventors: Edison, da Vinci. Edison is very much in the mould of commercial scientist and tinkerer. da Vinci is a wildcard, he’d probably go mad in today’s world because there would be so much he could play with.
There are no writers, musicians, etc. Leonardo wasn’t been chosen for his artistic prowess. This is due to my natural bias, obviously. Look, I’d love to have Douglas Adams or John Gielgud or Bach back, but honestly, would the world be much different today without Beethoven? Not for most people. Would the world be much different today without Kepler, Shannon, Stallman or Turing? Hell yes. If the OP had asked for a larger group of people or placed quotas, that would be a different story. (Now you know why quotas are important for diversity…)
Btw, I’m pleasantly surprised no-one here has mentioned Shakespeare.
It’s not been discarded, it’s been improved. Newton would agree with the improvements. Anyone who knows anything about science knows that it is a hodge-podge `sequence’ of improving approximations to the truth.
Typhoid Mary?
Huh? Did you have to sit through a few too many poor student productions or something? I’d clone the man in a second - seems to me that he’s one of the few who’d actually be able to contribute something. I mean, aside from recently deceased scientists who could rapidly catch up with their fields, most everyone else is a product of their respective times. I think the artists have a huge advantage in this little contest.
-the e team
(that would be ellis typing and eonwe giving the “ok” to the views espoused therein. cause it’s too much effort to log out and back in again.)
I’m well aware of that, thanks. Having not read any biographies of Newton myself, I had in mind a comment made by Cecil in a column about Newton’s apparently life-long virginity:
“Ninety percent of what he obsessed about–alchemy, biblical prophecy, and religious disputations were among his lifelong passions–was rubbish. The other ten percent, the stuff he did for laughs, I suppose we might say, took six thousand years of disjointed fumbling and made it into a science. Two sciences, actually, physics and to a large extent mathematics.”
I’m not saying he’s not worthy of consideration. I meant he might not be happy that alchemy is less than a booming field of study these days.
PT Barnum - 500 channels & plenty to watch.
Jesus - Can I get a witness?
JS Bach - the Colossus with one foot on Art & the other on Mathematics.
Shakespeare - greatest non-fiction writer.
Churchill - would tell us what is.
James Madison - would tell us what should have been.
Rousseau - would choke Postmodernism with a fresh serving of Natural Whoop-Ass.
Rutherford - the genius at organizing other geniuses.
Temujin - no doubt, would find way to offer alternative to Microsoft.
Gehrig - A freakish machine of an athlete (but only because Eddy Merckx isn’t yet dead).
For my list, I consider the greats whose lives were cut short:
The Mathematician Evariste Galois:
http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Galois.html
Killed in a duel, at a young age, his contributions to the development of Group theory were cut short! Even so, what was left, was enough for him to be recognized as one of the greatest mathematicians of the era.
Schubert, so he will finish the "Unfinished symphony”
Mendelssohn, (Jacob Ludwig) Felix Just because it is one of my favorite composers and had to die at 38.
Even younger: Mozart.
From the movie business: Irving Thalberg.
The great “boy wonder” producer died at 37!
Jim Henson.
James Dean.
Edgar Allan Poe, born in Boston, Jan. 19, 1809, died Oct. 7, 1849!
Louis Slotin 1910 – 1946
http://www.cns-snc.ca/history/pioneers/slotin/slotin.html
Jesus, but I fear everybody, believer or unbeliever, will be disappointed.
My picks:
Religion/Morality
Jesus
Buddha
Arts
T.S. Eliot
Shakespeare
Science
Einstein
daVinci
Politics
Washington
Lincoln
Multi-Category
Franklin
Jefferson
I’d clone ten Elvis impersonators.
I’d clone Abraham, Jesus and Mohammed so we could the religious thing sorted out.
I’d clone Ted Williams to get his remains out of the clutches of the freezer company.
I’d clone Babe Ruth and have the Cleveland Indians’ sign him.