Mary Lincoln. Wife of Abraham Lincoln, a woman of ferocious temper, who was once seen chasing the future president down a road waving a kitchen knife.

Lillian Russell. Famous actress and beauty of late 19th century America. She liked to ride through Central Park on a gold-plated bicycle, its spokes studded with diamonds, rubies, and emeralds. She got married several times, but liked to play poker on her wedding nights rather than going to bed.

'Calamity Jane' (Martha Jane Canary), another woman who liked to dress as a man, and who was variously employed as amueskinner, US Army scout, wagon freighter and Indian fighter (so she said anyway).

Molly Brown, fabulously wealthy and vulgar millionairess whose voice, it was said, was like a train whistle, and her gowns resemblec Christmas trees. She became a heroine after she survived the sinking of the Titanic.

Flora Sandes. Englishwoman who joined up as a nurse in WW1 and ended up serving as a soldier in Serbia. another woman who liked to dress as a man (there were a lot of them about).

Another Eleanor (Roosevelt)

In science, Marie Curie, winner of two Nobel Prizes.

In Medicine – Rebecca Lancefield, Virginia Apgar and Helen Taussig.

In legend – Helen of Troy

For Byzantine intrigue: Theodora, actress, courtesan and wife of Emperor Justinian.

For Rennaisance intrigue: Lucrezia Borgia.

For class in the face of adversity: Jackie Kennedy and Laura Bush

Founding Mother – Abigail Adams.

For Cambodia, I found a site that has famous women authors from Cambodia. You need to join the site to read the entire article about these three women, but the teaser has enough information to see if this might work for you.

For Thailand, I liked the interview with Dr. Pusadee Tamthai, which I linked below. She sounds great. (link below)

For Laos, I liked the speeches of Ms Onechanh Thammavong, a Member of Parliament. (in Laos) She's given speeches for the UN. (I linked her speeches below)

Zenobia. queen of Palmyra, she built a powerful empire in the east. Eventually she rebelled against rome and was defeated, taken to Rome in chains, she retired and married a Roman.

Saint Brigit of ireland. She founded the first the first nunnery in Ireland at Kildare, which became a double monastery for monks and nuns, famous as a centre of learning all over Europe. She founded churches throughout Ireland.

Hilda, abbess of Whitby, a powerful churchwoman who presided over the Synod of whitby in 666.

Empress Wu. A concubine who became empress of china, and ruled for many years as regent for her son.

Aefelflaed 'lady of the Mercians' the daughter of King Alfred, who fought against the Vikings in the 9th century AD.

Hildegarde of Bingen, a German nun who was a composer, scientist, and mystic. Wrote many books, and gave advice to the popes of her day.

Matilda of Tuscany, who ruled much of Italy in the 11th century, and fought on the side of the Pope against the Holy roman Emperor.

empress Matilda, the daughter of King henry I of england, who made a determined bid for the throne of england in the 12th century, and fought her cousin Stephen for the throne for many years.

Queen Blanche, mother of King Louis IX of France, who acted as regent for her son for many years during his childhood.

Catherine if Sienna. A nun who was a mystic and who gave advice to two popes.

Saint Bridget of Sweden. Another nun who was also a composer and who gave influential advice to the popes of her day.

Christine de Pisan, the first European woman known to have earned a living through writing, she wrote many books on many subjects. Her last work was a poem in praise of Joan of Arc.

Joan of Arc, who led the French armies against the English in the Hundred Years War, successfully raised the siege of Orleans, and crowned the Dauphin King of France.

Isabella of Castille, who married Ferdinand of Aragon, and thereby untied Spain under one rule. She financed christopher Columbus in his voyage in which he accidentally discovered america.

P.S. Cleopatra (mentioned in an answer above) was a great woman, but she was BC, not AD.

Oops, that's 11.