In London, thousands of people gathered in a square near parliament and Big Ben on Saturday.
They left white posters covered with red paint that looked like blood in a small park before starting a march through the capital towards Trafalgar Square, where a large rally was planned.
Some carried posters showing pictures of George Bush, calling the US president the "world's No 1 terrorist".
Other posters pictured Tony Blair, the British prime minister, saying "Blair must go!"
Police shut down streets in the heart of London's shopping and theatre district for the demonstration, which organisers hoped would attract up to 100,000 people.
In Stockholm, about 1000 demonstrators gathered for a rally before a planned march to the US embassy.
Some protesters carried banners reading "No to US warmongering" and "USA out of Iraq", while others held up a US flag where the white stars had been replaced by dollar signs.
Opposition to war
Elsewhere, global demonstrations began with smaller numbers than expected.
In Australia, about 500 protesters marched through central Sydney, while about 2000 turned out in Tokyo.
Students join a peace march
in Sydney, Australia
In Turkey, about 3000 protesters gathered on the European and Asian sides of Istanbul, police there said.
"Murderer USA," read a sign unfurled by a communist in Taksim Square in European Istanbul.
In Pakistan, hundreds of people held anti-war rallies in several cities, chanting slogans such as "Down with America!"
In South Korea, which has the third-largest contingent of foreign troops in Iraq after the US and Britain, up to 3000 demonstrators were expected to gather in Seoul on Sunday.
A rally was planned outside the US embassy in Malaysia's capital, Kuala Lumpur, on Sunday.
Anti-war demonstrations were also planned on Saturday in several Spanish cities, as well as in Austria, Germany, Greece and Denmark.