More than 7000 people marched through downtown Chicago on Saturday in one of the largest protests in the United States, saying the war diverts money from domestic needs and demanding the US pull out of Iraq.
Martha Conrad, 54, said: "I'm against this war, I'm against the torture."
"We're doing this for the people of Iraq."
Many of the weekend demonstrations in Australia, Asia and Europe drew fewer people than anticipated.
In London, police said 15,000 people joined a march on Saturday from Parliament and Big Ben to a rally in Trafalgar Square.
The anniversary last year attracted 45,000 protesters in the city.
In Japan, anti-war rallies stretched into a second day on Sunday, with about 800 protesters chanting "No war! Stop the war!" and banging drums as they marched peacefully through downtown Tokyo towards the US embassy.
A day earlier, about 2000 people rallied in the city.
Bush came under criticism
for the US-led invasion of Iraq
Organiser Ayako Nishimura said: "The Iraq war was President Bush's big mistake, and the whole world is against him.
"Iraq must decide its own affairs."
Elsewhere on Sunday, anti-war protesters demonstrated outside the US Embassy in Malaysia, and at least 1000 people turned out in Seoul, South Korea, which has the third-largest contingent of foreign troops in Iraq after the US and Britain.
Iraq - a worse place
In London, Rose Gentle, whose soldier son Gordon, 19, was killed by a roadside bomb last year in Basra, southern Iraq, said Tony Blair, the British prime minister, has made Iraq a worse place for the Iraqi people.
"Every day you hear of new deaths," she said.
Britain, the United States' strongest supporter in the Iraq war, has about 8000 soldiers in Iraq but plans to pull out 800 of them by May.
Donald Rumsfeld, the US defence secretary, answered critics of the war in a guest column in Sunday's editions of The Washington Post, saying that turning away from Iraq would be "the modern equivalent of handing postwar Germany back to the Nazis".
Rumsfeld has again defended
the US presence in Iraq
"It would be as great a disgrace as if we had asked the liberated nations of Eastern Europe to return to Soviet domination because it was too hard or too tough or we didn't have the patience to work with them as they built free countries," he wrote.
More than 1000 people gathered on Saturday in New York's Times Square near a military recruiting station, which was guarded by police.
Wael Musfar of the Arab Muslim American Federation, who addressed the crowd, said: "We say enough hypocrisy, enough lies, our soldiers must come home now."
Participants chanted, "Stop the US war machine, from Iraq to Korea to the Philippines".
Many attendees emphasised that they support the troops.
Jose Avila, 36, said: "I have friends in Iraq and I just want them to know that I may not be able to support them there, but I can here."
In Chicago, a bystander with a red, white and black Iraqi flag flung across his shoulders said he came to show he backed Bush's policies in Iraq.
Ryan Stiles, 33, said: "I support freeing Iraqis from tyranny."