Before and during the Cold War, Americans and their leaders were in love with the first lady of China, then Taiwan, American-educated Soong May-Ling, better known as Madame Chiang Kai-Shek (she and her husband were Time's "Man and Wife of the Year"). She was never quite as popular at home, being the wife of a brutal dictator.
US president Rutherford B Hayes is rather obscure and unremarkable in American history, best known for his Badass Beard and the probability that he stole the election that brought him to office (hence the nickname "Rutherfraud"). However, he is a national hero in Paraguay, having served as an arbitrator after the War of the Triple Alliance in South America that had pitted Argentina, Brazil and Uruguay against them. Hayes' ruling in favor of Paraguay, allowing it to keep a large swath of disputed territory in the center of the country, forever immortalized him in the country's history as their savior. He has a city (Villa Hayes) and a department (Presidente Hayes) named after him, as well as many schools, roads, and even a soccer team.
Most Frenchmen have never heard of Frédéric Bastiat; his works are most popular with American libertarians and anarcho-capitalists.
The same may apply to his friend and contemporary, the Belgian economist Gustave de Molinari. (They were in the same philosophy club).
Austrian Emperor Franz Joseph is incredibly popular in Israel due to his attempts to squash ethnic nationalism in his empire and Austria-Hungary being one of the friendliest nations in Europe for Jews, especially for poorer ones in Central Europe who needed to get out of the anti-Semitic Russian Empire but couldn't afford to go to America or live in Western Europe. There's a reason you can still find parents in Israel that name their son "Franz Joseph".
Saladin is one of the most celebrated military leaders of all time, as a chivalrous Muslim warrior, and a Magnificent Bastard by the Crusaders. Coincidentally, this lionization did not originate in the Middle East, but in Europe. Of course, his fellow Kurds also think highly of him, as he's a very well-known Kurd (who many probably didn't even know was Kurdish at all), and Arabs lionize him as well (since the lands he ruled are/were predominantly Arabic-speaking and his armies were composed in large part of Arab troops), which gets them into occasional tiffs with Kurds (particularly over Arab nationalists' use of the Eagle of Saladin as a symbol of their movement).
The friendship between Filipino national hero Jose Rizal and Austro-Hungarian writer Ferdinand Blumentritt is the stuff of legend here in the Philippines. In turn, Rizal is popular in Austria and Hungary. William Howard Taft's stint as Philippine Governor-General is also memorable here.
Voltaire the philosopher was very popular among the Russian aristocracy during the reign of Catherine the Great.
Dr. Norman Bethune, a war doctor virtually unknown in his home country of Canada during his lifetime, is considered an icon in China for his medical service during the Second Sino-Japanese War. He gained international attention when Chairman Mao Zedong published his essay In Memory Of Norman Bethune which had been a part of the required reading in Chinese elementary schools since the '60's. Dr. Bethune is also one of the few Westerners to have statues erected in his honour.
Canada only noticed Bethune after befuddled travel agents started wondering why all those Chinese tourists want to go to the no-name town of Gravenhurst, Ontario.
No matter how spotted his career, Filipinos will always think fondly of Douglas MacArthur as the man who liberated them from the Japanese in World War II.
The Japanese themselves seem to think fondly of MacArthur over his Shogun-esque rule of their land. Over in the west, he's remembered more as the guy who refused to acknowledge Emperor Hirohito when the latter tried to apologize for his actions.
Napoleon Bonaparte is very popular among Jews and in Israel, mainly because of his Jewish emancipation policies.
He is also big in Poland.
Cyrus The Great is also popular in Israel, for allowing Jews to return to their ancestral homeland.
Karl Marx was a German writing in the U.K. As you probably already know, he and his ideas became very big in Russia and China during the twentieth century. Strictly speaking, they did get back to Germany, but by way of Russia.
Not just by way of Russia, as a large part of his ideas (without the additions by Lenin, Stalin and Mao) were studied and adopted by various Socialist and Social Democratic parties, notably the SPD, one of the major parties in Germany for the past 150 years.
W. Edwards Deming was largely an obscure figure in his native United States. In Japan, however, he was the man who revolutionized management. His ideas began to be recognized in United States only by late 1980s, when it looked as if Japanese firms were going to drive US companies out of business.
William Ewart Gladstone, a 19th century British prime minister, is considerably more popular and better known in Bulgaria than in his native country for condemning Ottoman rule over Bulgaria and the "Bulgarian horrors" (the massacre of between 15 and 20 thousand Bulgarians after the unsuccessful April uprising).
While an obscure figure in his native United States, Adolf A. Berle is beloved in Latin America as a major architect of the "Good Neighbor policy".
Christopher Columbus still is viewed favorably amoung Italian Americans and in Italy. Most Americans on the other hand view Columbus day as "just another day off" and not care much about the person himself, while both Native Americans and African Americans consider him to be the man who started the mass genocide and exploitation of their people, along with laying the foundation of the slave trade, respectively and call for Columbus day to be abolished outright.
Genghis Khan is revered in Mongolia and deemed worse than Hitler in the rest of the former Mongol Empire. However, outside of the Empire, he's thought of as a major-league Bad Ass and an excellent statesman.
US diplomat Henry Kissinger is often maligned by many in America and around the world (especially in Third World countries with leftist governments today) due to his support of brutal third world anti-Communist (more like anti-leftist) dictatorships in Pakistan, Indonesia and South America (more specifically Chile under Pinochet and Jorge Videla's junta in Argentina) with severe human rights violations along with his role in the secret bombing of Cambodia during the Vietnam War, all of which have left many, noticeably Christopher Hitchens to consider him a potential War Criminal or tie him to many conspiracy theories. However, he is much more liked in China due to his role in helping open up relations between the US and China during the Nixon years.
Richard Nixon himself counts as an example in China as well. When this troper's Chinese parents first immigrated to the US, they were very surprised to learn that Nixon's legacy in the US is not as a well-respected, internationalist elder statesmen but rather as President Corrupt who nearly irrevocably tarnished the office he held as a result of Watergate.
Mikhail Gorbachev is thought of in Western nations as a well respected statesman who ended the Soviet Union. In particular, he is practically a national hero in Germany for bringing down the Iron Curtain that went straight through the country. The Russian population has quite a different opinion of the man, seeing him as a weak leader who kept giving the West concessions and ended Russia as a superpower, and those who are nostalgic for Communism — or even, in many cases, just democratic socialists — positively HATE him. When he ran for president of The New Russia in 1996, Gorbachev won a grand total of 0.51% of votes. An Urban Legend has it that, during a meeting with voters, he was punched in the face.
Lampshaded in a Pizza Hut advert in Russia, where he and his grand-daughter walk into a namesake outlet. The patrons vividly debate his legacy, eventually concluding they're all eating at Pizza Hut because of him.
Of course, he ended the Soviet Union inadvertently.
Similarly, Tony Blair seems to be MUCH more popular in the US than he is in his native UK, where his decision to work closely with George W Bush in the invasions of Afghanistan and Iraq was met with wide condemnation by the British people, ultimately all but forcing him from office. He has even had to cancel recent public appearances in the UK to publicise his new autobiography due to the "hassle" caused by protesters, and his party are now trying to distance themselves from the Blair era as quickly as possible.
He's also very popular to this day in Sierra Leone due to his having (not enthusiastically initially) stopped a civil war there by sending the army in (the army were sent in on a limited mission but decided to intervene aggressively, Blair's role amounted to backing them once he found out about it). Seriously, they build statues to him, you won't find that in the UK.
Margaret Thatcher is universally respected as an important stateswoman in most countries and an icon of feminism. In the U.K. her legacy is more polarizing. To the upper class and big companies she is revered as a visionary politician. To the middle and lower classes, Scotland, and all Oop North, who suffered under her economic policy, she is hated to this day. When her death was announced in early 2013, people literally danced in the streets and threw Maggie Thatcher Death Parties. The song "Ding Dong, the Witch is Dead" was requested (and played) constantly on radio stations.
She's hated in Ireland and Argentina as well. The Argentines hate her over the Falklands War and the Irish hate her for the South Africa-esque oppression of Catholics in Stroke Country.
Many Germans also tend to remember her as the most prominent opponent of German Reunification after the Wall fell.
George W. Bush is considerably more popular in Georgia (the country) than in the U.S., due to his pro-Georgian foreign policy and having danced to Georgian music once. Reportedly, he's even sometimes considered a bit of an Mr. Fanservice in Georgia. Figure that one out.
He's also really popular in some parts of Africa for the understandable reason that he sent a ton of AIDS relief there.
While his approval rating in America was around 30% during the last few years of his tenure, his approval rating in India stayed around 60%.
Bush is very popular in the Kurdish territories of Iraq. Since the invasion the Kurds have been able to form there own semi-self governing state in the north of iraq. He's popular enough that they sell T-shirts with his picture on them.
Also in Kosovo and neighboring Albania for supporting Kosovar independence, despite the fact that he couldn't even get their names right (he called them "Kosovoans"). The Albania example also extends to other American presidents in general (for example, "Bill" and "Hillary" are still very popular baby names there).
In a truly bizarre example, former Premier of Ontario, Dalton McGuinty. Often considered bland (or, to his opponents, "Premier Dad", due to his "nanny state" policies) in his home province of Ontario, he is considered "handsome and charismatic" in China. FTA:
"Who else is as good at working a Chinese room?" a Canadian businessman was asked during a luncheon in Nanjing. "Exactly," he replied, mistaking it for a rhetorical question.
In stark contrast, back home in Canada, several comedy shows have made fun of McGuinty's striking resemblance to Norman Bates◊.
Congressman Ron Paul has a rather divisive public image in the US. Around the world however, he is much more liked. This is probably due to his foreign policy views of isolationism and non-interventionism, as the US foreign policy has drawn criticism from many around the world.
President Barack Obama is generally more popular in Canada, Australia and the European countries than in certain areas of the United States.
Muammar Gaddafi. He was hated in the Western world and in Libya, where his own people eventually killed him. In sub-Saharan Africa, he is still seen as a hero by many people (including Nelson Mandela), mostly because they remember him as a prominent figure of the Non-aligned movement.
Woodrow Wilson goes through Popularity Polynomial in his home country, though he generally maintains a good reputation despite the heavy Values Dissonance associated with him. Most Eastern Europeans, meanwhile, adore him, since he was integral in breaking up the Austro-Hungarian Empire. Tell a Serb that Wilson's racial policy wasn't even Fair for Its Day, and he'll punch you.
Richard Nixon, thanks to 'Gate and 'Nam, is arguably the most hated former President in US history... except among American Indians, who revere him as a hero who did more to improve their plight in his six years in office than every other President before him put together. He appointed a Mohawk as Commissioner of Indian Affairs, and signed laws saving Indian resources and returning many Indian lands to their original owners. Most of all, he put a stop to the horrific policy of Termination, which forced Indian people to "assimilate" by relocating them into unfamiliar cities. There's a reason the Paiutes of Pyramid Lake, Nevada named their capital city Nixon.
In a really bizarre example, Snooki is a pop culture icon there. Yes, travel down the streets of Everton or Wavertree and there will be a fair few Snooki lookalikes (Snookalikes?).
Lior Suchard, the Israeli psychic who recently became immensely famous in the States, was pretty much forgotten in Israel after he won the original version of The Successor (people jokingly remarked back then that Uri Geller’s next trick was to make Suchard disappear).
Muhammad Ali, while one of the most respected boxers of all time, was very popular back in the United States, but was huge in Zaire (Now known today as The Democratic Republic of the Congo), after his "Rumble in the Jungle" match against George Foreman held there c. 1974. Google "Ali Bomaye".
You can add Italy to the list of countries that still love Hilary. In fact, there is one exclusive compilation album not available outside of Italy.
One wonders if her popularity in Italy came before or after The Lizzie McGuire Movie was set in Rome.
Bella Thorne has lots of Japanese fans. Some of her tweets are replied by Japanese fans. She even retweets her Japanese fans who did the tweets in English.
Tanya Melissa Makse (or Tanya Makse on modelmayhem.com - she shortened her name, this isn't a stage name), a model/actress from Kelowna, British Columbia, Canada is extremely popular in Southport, Liverpool, and the outlying backwaters that are Formby, Bootle, Litherland, Ormskirk, Skelmersdale. Along with Wigan, Bolton, Bury and much of Greater Manchester too. Also popular Oop North too.
Taylor Kitsch is considered an unmarketable actor in the United States and his native Canada after having led two high-profile flops (John Carter and Battleship). But in Europe and Asia, both films were very successful and he's averted career troubles by getting more offers in projects with broad foreign appeal.
The late actress Deborah Raffin became a huge star in China when her TV-movie Nightmare in Badham County was a big hit there.
Soap actress Thalia is a superstar in the Philippines thanks to its exposure to her shows like Maria Mercedes, Maria La Del Barrio, and Marimar. Marimar and Maria la del Barrio were popular enough to get their own Foreign Remake.
Inexplicably, the actress who played the villain of Marimar, Chantal Andere, had her own fans in the Philippines via Memetic Mutation.
American illusionist, Val Valenteno better known as The Masked Magician became very popular in Brazil following his television specials of revealing the secrets to several magic acts. He apparently was also very well liked in Japan.
Jan-Ove Waldner: Legend in Sweden, even more popular in China.