But governments told their citizens not to allow security concerns to mar their enjoyment of the occasion - and many thousands of revellers took their advice.
"
No terrorist is going to
keep me away from these celebrations
"
Mike Hemmings, Edinburgh's Hogmanay
More than 500,000 New Yorkers shrugged off domestic terrorism concerns and the threat of war with Iraq to usher in 2003 in Times Square.
The massive party was given the official theme "Hope for Courage" but the high police presence, sealed manhole covers and myriad other security checks were a constant reminder of the troubles clouding the celebrations.
Security checks
Security had never been tighter for New York's big party, said BBC New York correspondent Emma Simpson.
Revellers were all searched, and no bags or alcohol were allowed into Times Square.
Rooftop sniper teams were deployed, rubbish bins removed, and all planes banned from flying low over the city.
"Some people will be inconvenienced, some people will be annoyed. But that's the price we pay for living in a dangerous world," said New York Mayor Michael Bloomberg.
Party goers did not seem put off by the tighter security.
"I've wanted to see this since I was three," said 14-year-old CJ Reeves from Texas. "It's my dream come true."
Europe celebrates
Revellers in Europe also braved tight security and icy weather conditions to ring in 2003.
Some 200,000 Parisians turned out to celebrate in the Champs-Elysees, flanked by hundreds of police officers.
Only last week, the terror threat to Paris was highlighted by the arrest of an airport baggage handler whose car was found to contain weapons and explosives.
In Berlin, up to 700,000 people crowded around the historic Brandenburg Gate at the stroke of midnight, braving temperatures as low as -8C.
Freezing conditions did not stop Muscovites, either, from taking to the streets to bring in 2003.
Revellers in the UK had no opportunity to celebrate in traditional fashion in London's Trafalgar Square, which is closed for renovation, but celebrated in style in many other cities, including Edinburgh and Newcastle.
Mike Hemmings, a 45-year-old at Edinburgh's Hogmanay street party said: "No terrorist is going to keep me away from these celebrations."
'Full of hope'
In Indonesia, President Megawati Sukarnoputri spent New Year on the island of Bali, hit by a devastating bomb attack in October.
"I ask all Indonesians to live in peace and security," she told crowds on Kuta beach, just a few blocks from the scene of the bombings.
In Australia, hundreds of thousands of people watched a fireworks spectacular around Sydney harbour.
"After... all this talk about terrorism it is so good that Australians overcame adversity," said Sydney's Lord Mayor, Frank Sartor.
Other festivities were marked by a mixture of joy, sorrow and anger: