In Europe, where more than 200,000 people thronged a Berlin rally in 2008 to hear Barack Obama speak, there's disappointment that he hasn't kept his promise to close the military prison at Guantanamo Bay, and perceptions that he's shunting blame for the financial crisis across the Atlantic.
In Mogadishu, a former teacher wishes he had sent more economic assistance and fewer armed drones to fix Somalia's problems. And many in the Middle East wonder what became of Obama's vow, in a landmark 2009 speech at the University of Cairo, to forge a closer relationship with the Muslim world.
In a world weary of war and economic crises, and concerned about global climate change, the consensus is that Obama has not lived up to the lofty expectations that surrounded his 2008 election and Nobel Peace Prize a year later. Many in Asia, Africa, the Middle East and Latin America were also taken aback by his support for gay marriage, a taboo subject among religious conservatives.
But the Democrat still enjoys broad international support. In large part, it's because of unfavorable memories of his Republican predecessor, George W. Bush, and many people would still prefer Obama over his presumptive Republican challenger Mitt Romney.
"We all had high hopes for him," said Filomena Cunha, an office worker in Lisbon, Portugal, who said she's struggling to make ends meet. "But then things got bad and there's not much he can do for us over here."
Obama's rock-star-like reception at Berlin's Victory Column in the summer of 2008 was a high point of a wildly successful European campaign tour. The thawing of a harsh anti-Americanism that had thrived in Europe was as much a reaction to the Bush years as it was an embrace of the presidential hopeful.
Those high European expectations have turned into disappointment, largely because of the continued U.S. military presence in Iraq and Afghanistan and Obama's failure to close Guantanamo Bay in the face of vehement congressional opposition.
Foreign policy expert Josef Braml, who analyzes the U.S. for the German Council on Foreign Relations, said many Germans give Obama too much of the blame because they don't understand the limits of his powers.
"There's a lack of understanding both of how the system of checks and balances works — or doesn't work any longer — and a lack of understanding of how big the socio-economic problems in the United States are, which cause the gridlock," Braml said in a telephone call from Greece, where he was on vacation.
Obama's views on Europe's financial crisis also have rankled some on the continent. In September, he said the crisis was "scaring the world" and that steps taken by European nations to stem the eurozone debt problem "haven't been as quick as they need to be."
The Obama administration describes the eurozone crisis as a European problem that needs a European solution. The U.S. and Canada last month refused to participate in boosting the International Monetary Fund's financial resources to manage the crisis.
"I think people see through his game to put the blame on Europeans — I think Germans and Europeans still know where the economic crisis had its beginning," Braml said. "That's just finger-pointing, not doing a fair analysis of the dire situation in the U.S., but I can understand Obama is doing that because he wants to get re-elected so they need to shift blame around on the Republicans or the Europeans."
Mehmet Yegin, a specialist in Turkish-American relations at USAK, the Ankara-based International Strategic Research Organization, said Europe still sees Obama as superior to Romney, "because they primarily evaluate Romney as a Republican and their memories about George W. Bush linger."
Many in the Mideast also would like to see Obama win a second term, though they feel he has not lived up to his Cairo speech, in which he extended a hand to the Islamic world by calling for an end to the cycle of suspicion and discord.
Obama has been the U.S. president "least involved in the Palestinian issue," said Mohammed Ishtayeh, an aide to Palestinian President Mahmoud Abbas.
"We were very optimistic when Obama was elected. He talked in his meeting with us without looking into his notes; that tells how much he knows about our issue," he said.
But since Obama made his Cairo speech, Ishtayeh added, "he found his hands tied and couldn't make much progress."
The Palestinians have refused to conduct peace talks while Israel continues to expand its settlements in the West Bank and east Jerusalem — areas claimed by the Palestinians. Officials have quietly given up hope for any sort of breakthrough until after the presidential election.
Obama also has a strained relationship with Israel, where Bush was popular. Obama and Israeli Prime Minister Benjamin Netanyahu have been cool to one another in their handful of meetings. Obama's Mideast envoy, former U.S. Sen. George Mitchell, made no progress during two years of frequent meetings with both sides before quitting last year.
Despite the chilly relations between Obama and Netanyahu, overall ties between the allies remain strong. The U.S. has backed Israel on several key occasions at the United Nations, for instance, helping block a Palestinian attempt to join the world body last year without a peace deal and fending off attempts by other countries to charge Israel with human rights abuses.
"Concerning Israel, he has proved that he is not absolutely rigid but is willing to reconsider when confronted with facts that he would not have expected," said Avraham Diskin, a political scientist at Jerusalem's Hebrew University.
"He began very inexperienced on all fronts, but he is a very intelligent person and Israelis see that," Diskin added.
In Iraq, site of the war that fed much of the international community's dislike of Bush, Obama has received some credit for pulling out combat forces last year.
"President Obama has removed so much of the cowboy image of America that has been imprinted in the mentality of Iraqis by Bush," Baghdad lawyer Raad Mehsin said.
But Carawan Ahmed, a high school teacher in Iraq's northern Kurdish capital of Irbil, said Obama has ignored the Kurdish minority, which continues to struggle against the Shiite-dominated government.
"When Democrats, including Obama, are in power, we lose the sympathy and support from America. To be frank, the Republicans protected the Kurdish people, while Obama's administration is not," Ahmed said.
In Mogadishu, former schoolteacher Fadumo Hussein retains a shaken support for Obama, but disapproves of the mounting casualties from U.S. drone attacks on Somalia's al-Qaida-linked insurgency while the country's humanitarian need is neglected.
"He only sent drones, not enough assistance," Hussein said. "We don't need bombs, but other means of assistance."
Obama remains popular in Japan, one of the United States' closest allies, though that may be a matter of style over substance, said Koichi Nakano, political science professor at Sophia University in Tokyo.
"The Japanese like Obama. Maybe they don't know all that much about him, but I guess he continues to be seen as a youthful, energetic, charismatic leader," he said.
America's stature has taken a hit in Japan since the 2008 financial meltdown, which highlighted the excesses of U.S.-style capitalism to many Japanese. They also fret about the increased attention Washington is giving China, which supplanted Japan as the world's second-largest economy.
While still widely admired in Japan, the U.S. "comes across as a more divided country and less self-confident, more concerned about its social harmony and less about the outside world," Nakano said. That's translated into "a general perception that Obama may not be that interested in foreign policy, period."
Obama, however, has tried to build on America's connections to Asia as authoritarian China grows. Adam Lockyer, a lecturer at Sydney University's U.S. Studies Center, said those efforts have been received more warmly in Australia because of who is in charge.
During a visit last year in which he received an overwhelmingly popular reception, Obama announced that up to 2,500 U.S. Marines will be stationed in Australia's north for joint training exercises. Australian government fears of a public backlash were never realized.
"The fact that Obama himself was making the announcement of U.S. troops in Australia quelled a lot of fears," Lockyer said. If Bush had made it, he said, "there would have been a lot more hostility."
"Democrat presidents tend to be a little bit more hesitant to define the world as good and evil, which tends to be more attractive to Australian ears," he said.
Don Melvin reported from Brussels, and Rod McGuirk from Canberra, Australia. Contributing to this report were Associated Press writers David Rising in Berlin, Ian Deitch in Jerusalem, Mohammed Daraghmeh and Dalia Nammari in Ramallah, West Bank, Malcolm Foster in Tokyo, Mazin Yahya in Baghdad, Abdi Guled in Mogadishu, Somalia, Hamza Hendawi in Cairo, Barry Hatton in Lisbon, Portugal, and Chris Torchia in Ankara, Turkey.