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 the president 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 was 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 summer 2008 was a high point of a wildly successful European campaign tour. The thawing of harsh anti-Americanism that had thrived in Europe was as much a reaction to the Bush years as it was an embracing of the presidential hopeful.
Those high European expectations have turned into disappointment, largely because of the continued U.S. military presence in Afghanistan and Obama's failure to close Guantanamo Bay in the face of congressional opposition.
Foreign policy expert Josef Braml, who analyzes the United States 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 socioeconomic problems in the United States are which cause the gridlock," Braml said in a telephone call.
Mehmet Yegin, a specialist in Turkish-American relations at USAK, the International Strategic Research Organization in Ankara, said Europe still saw 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 Authority President Mahmoud Abbas.