-quote-
Gives people a chance to pick and choose. You could serve it with a grilled vegetables and baby roasted potatoes. ... A couple of simple salads would make it a perfect dinner. ... I throw them all the time and we have a blast. ..
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2 Men:

http://t1.gstatic.com/images?q=tbn:2h59jgeOS53qgM:http://www.daviddarling.info/images/Descartes.jpg
Rene Descartes

http://t1.gstatic.com/images?q=tbn:8ClBVEcuPsDJkM:http://innovationmcr.files.wordpress.com/2009/09/thomas-edison.jpg
Thomas Edison

2 Women:

http://t3.gstatic.com/images?q=tbn:bnxryHSlYVYRRM:http://myersau.files.wordpress.com/2009/01/ellen-ochoa.jpg
Ellen Ochoa

http://t0.gstatic.com/images?q=tbn:g4lgB00TK2OE_M:http://www.noonewatching.com/archives/2007/10/margaret%2520mead.jpg
Margaret Mead

Why:
Each of these people has, through pure innovation, pushed the limits of what their chosen industry was capable of. I would ask Mead to moderate predetermined questions along with natural conversation to ensure that the dinner party stayed on topic.

If I had to pick only one, it would be a toss-up between Edison and Descartes. Edison would likely win if only one dinner party invite was allowed to be given; I think that guy must have some stories that aren't published ;)

If the four people wouldn't have to be a coherent group, I would pick:
- Dr Jackal @ Mr Hide. Not being bothered by the fact that they are both the same person, it would be very interesting to see a confrontation between the two. Would they immediately start a fight, or would they see some common ground in the fact they possess the same body?
- Maria Magdalena. I would have a zillion questions for her, to find out more about her intriguing period of time. Was Dan Brown right in his book, when he made Maria the center of worship? What's her take on the life of Jesus? Many interesting questions to ask, enough to fill an entire evening (and probably more)
- Joan of Arc. Strong woman, led her nation on revolt, was executed as a witch. I came across her name when researching another question here, and am now intrigued by her story. How did she end up getting accused of witchcraft? How does she see women suffrage in our current times?

A very diverse group of people, who probably wouldn't get along when all were at the same table. Interesting persons, nonetheless, and guaranteed to be a night to remember...

I would like to have my fantasy dinner party on All Hallows Eve this year!
My guest list would include Lord Byron, Edgar Allen Poe, Madeline Kahn and Laurie Cabot.

I figured that we could all meet at Byron's Villa Diodati on Lake Geneva.
We could start off the evening with some absynthe and story telling.

This would be a perfect mixture of people, stories and experiences. I think that Poe and Byron would be fascinated to meet Lauie Cabot since she is a real witch.
Madeline Kahn would have some great humor and fun experiences to throw into the group if things started getting a little too somber.

Something tells me that this group would make instant bonds and the most fantastical conversation... ever!

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Literary Fantasy Group:
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Robert A. Heinlein 1907-1988:
http://en.wikipedia.org/wiki/File:Heinlein-face.jpg
In my opinion, the greatest and likely most influential Sci-Fi and Libertarian novelist to date. He is also a veteran of the US Navy and among other things served as a radio communications officer on an aircraft carrier. His is credited with inventing the concept of the waterbed as well as dreaming up numerous sci-fi concepts that have eventually turned into modern technology. He was active in politics as a socialist, described himself to Asimov has a "flaming liberal" and over time became an individualist Libertarian with somewhat radical ideas about personal freedom.

Ayn Rand 1905-1982:
http://www.flickr.com/photos/wwwwwww/18243373/
Russian-American novelist famous for works such as "Atlas Shrugged" and "The Fountainhead". Immigrated from Russia to the US when she was 21, after experiencing changes wrought by the Russian. Often thought of as a Libertarian, she was founder of the Objectivism Movement and was fiercely in favor of capitalism, reason and limited. If the other guests could keep her from preaching and ranting long enough to engage in friendly conversation, she would be a fascinating dinner companion.

Mark Twain (Samuel Clemens) 1835-1910:
http://www.flickr.com/photos/whenlostin/3877067172/
American novelist and humorist. His biting wit and keen observations of the human condition would be an asset to any social gathering. His world travels and experiences during the formation of the modern Western world would make for years of fascinating stories. He was a licensed steam boat pilot of the Mississippi River, Secretary to the Territorial Governor of Nevada, a student of parapsychology and a journalist who covered the maiden voyage of a steam ship to the Sandwich Islands before they became known as Hawaii. He lived through the Civil War and the end of slavery.

Anne Louise Germaine de Staël-Holstein 1766-1816:
http://upload.wikimedia.org/wikipedia/commons/thumb/1/11/Madame_de_Sta%C3%ABl.jpg/427px-Madame_de_Sta%C3%ABl.jpg
French speaking Swiss novelist and intellectual who lived through the French Revolution and went on to become an intellectual antagonist of Napoleon. Famous for her sharp intellect at a time and culture when women were not widely respected for their brains. Strong advocate for women's rights. She associated and slept with and with many influential French thinkers and political players, including Talleyrand. She traveled extensively throughout Europe and owned property in the newly formed United States. Her remarkable experiences, sharp wit and outspoken nature would make her a hit at any dinner party.

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Political Fantasy Group:
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Thomas Jefferson (1743 – 1826):
http://upload.wikimedia.org/wikipedia/commons/4/46/T_Jefferson_by_Charles_Willson_Peale_1791_2.jpg
American revolutionist, lawyer and political activist. Primary author of the Declaration of Independence, founding father and Third President of the United States of America. This outspoken radical political thinker tremendously shaped the formation of our nation and is hugely responsible for our system of government. His knowledge of Latin, Greek, French and English would help the other guests communicate with Cleopatra. His heavily edited version of the New Testament (The Jefferson Bible) and dislike of mainstream church beliefs would help him to get along fabulously with the next dinner guest, Thomas Payne.

Thomas Paine 1737 - 1809:
http://upload.wikimedia.org/wikipedia/commons/2/2d/Thomas_Paine.jpg
Brilliant and revolutionary thinker, deist and pamphleteer. Considered a founding father of the United States and heavily influential on both the French and American revolutions. Author of the infamous "Age of Reason", a two part work that challenged the power of the church’s hold over intellectual and scientific thought and refuted the veracity of the bible. His other famous and highly influential works include "Common Sense", "The Rights of Man" and "Agrarian Justice". By his death in 1809 he had managed to offend so much of the world that his funeral was attended by only 6 mourners. This sort of rebellious firebrand would be certain to enliven the dinner party.

Baroness Margaret Hilda Thatcher 1925 - Present:
http://www.flickr.com/photos/quixotic54/3060881300/
Prime Minister of the United Kingdom from 1979-1990. This strong willed, powerful and sharp witted lady was raised by a politically active Methodist preacher and went on to become an Oxford trained chemist and crystallographer. She supported herself as a research chemist and scientist before her meteoric rise in politics. In Parliament she became an outspoken opponent of high taxes which she considered the precursors to socialism and communism. She was an enemy of income tax, trade unions and terrorism and a proponent of privatization of government controlled industries. Her successful handling of the Falkland Islands war transformed her abysmal public approval rating from 30% to 59%. Her support of Ronald Regan's military policies and placement of missiles on European soil likely helped bring about the end of the cold war. This powerful outspoken woman would make a great counterpart to the other guests at this dinner gathering.

Cleopatra VII 69BC - 30BC:
http://www.flickr.com/photos/tiffanysilva/3035481904/
Pharaoh and Hellenic warrior queen of Egypt, mistress of both Julius Caesar and Marcus Antonius. This powerful and beautiful manipulator changed the course of Western Civilization. During her rule she was believed by many to be the embodiment of Isis, Goddess of Wisdom. Her brains, beauty and historical experiences would entrance the other dinner guests. Her fluency in Greek, Latin and half a dozen other languages allowed her to gain insights into numerous cultures and would help her communicate with some of the other dinner guests.

George Clooney

I would invite science/tech historian James Burke simply because he uses his knowledge of the past to predict the future and would love to hear about what he has to say about it now that it's been well over 20 years since his last TV special.

http://www.youtube.com/watch?v=mB8_wPei2ZM

The 2nd Male I'd invite would be good-ole Jon Stewart to provide a little comic relief.

http://farm1.static.flickr.com/56/137570555_477db29ab5_o.jpg

As for the ladies I'd invite my two favourite Mahaloians @bunnyphuphu and @gno :D

What does it say that I find it easy to think of lots of men, but I struggled to think of any women?

Well, without too deep thought into the subject I will go for two dead men that I'd have loved to have met, and two living women that I'd love to meet someday.

1) Richard Feynman

http://www.phys.ufl.edu/~sps/images/feynman.jpg

One of the greatest scientists of the twentieth century, and also bags of fun to boot. Apart from being a top notch physicist, he took part in the Manhattan project to build the atom bomb in World War II, investigated the Challenger Space Shuttle disaster, taught himself to play the bongos and break into safes, and had lots of insightful things to say about life, the universe and everything. (Sadly Douglas Adams isn't going to make my list, though I'd love to have him to dinner too.)

2) John Maynard Keynes

http://static.howstuffworks.com/gif/trickle-down-in-down-market-2.jpg

One of the greatest economists of the twentieth century. Played a major role in understanding and resolving the Great Depression, and was one of the architects of the global economic system after World War II. Like Feynman, he had lots of interests outside his work.

The two of them together would make for fascinating connversations, because they came at things from very different angles. For example, Feynman was pretty sceptical about the social sciences, and impatient with the workings of politics, management etc. While Keynes was the ultimate political insider, and not just a thinker but very much involved in making deals, figuring out how to get things done etc. Between them they'd have lots to say about life today.

3) Natalie Portman

http://img2.timeinc.net/instyle/images/2007/parties/103107_portman_300X400.jpg

Apart from being an actress and a very attractive woman, she's also bright and engaged in the world. In that picture above she's speaking to students at Harvard about microfinance, a cause that she's been deeply involved with. So she'd fit right in with the flavor of this dinner party.

4) Aung San Suu Kyi

http://upload.wikimedia.org/wikipedia/commons/2/26/Burma_3_150.jpg

For this particular dinner party, I gotta have an inspirational female leader. Ok, if you didn't insist on two men and two women, Nelson Mandela or Mahatma Gandhi would likely be on the list. But she's the nearest we have to a female Nelson Mandela, and would bring an amazing perspective to the discussion.

Ok... I'm not sure if this a dinner party so much as a Summit Meeting. :)

But it surely would be fascinating, eye-opening and inspirational. Even if I entirely failed to understand a good deal of what they were talking about! (Feynman and Keynes both having being described at various times as the smartest people on the planet, and Keynes as unearthly in his intelligence!)