NEW YORK — Nearly a million revelers crowded New York’s Time Square to witness the traditional dazzling ball drop, fireworks lit up Australia’s Sydney Harbor and communist Vietnam held a rare Western-style countdown to the new year as the world ushered in 2011.

In Europe, Greeks, Irish and Spaniards partied through the night to help put a year of economic woe behind them, and Japanese revelers released balloons carrying notes with people’s hopes and dreams.

In New York, a crystal ball with 32,000 lights descended at midnight, setting off a wild and noisy confetti-filled New Year’s celebration — the country’s largest — at the crossroads of the world. And it all happened just days after a debilitating blizzard paralyzed the city and the surrounding area.

All around the United States, people said they were setting aside concerns about the economy, bad winter weather and even potential terrorist threats to ring in 2011 at large and small gatherings.

Even more than most years, New York was in the spotlight as it battled back from a severe snowstorm and security concerns eight months after a Pakistani immigrant tried to detonate a car bomb in Times Square. Police said the city wasn’t the target of a New Year’s Eve terror threat, but they had a strict security plan in place, with sealed manhole covers, counter-snipers on rooftops and checkpoints for partygoers.

Mayor Michael Bloomberg has endured days of withering criticism for the city’s slow response to the Dec. 26 storm, which dumped 20 inches of snow. But the president of the Times Square Alliance said holiday tourists helped clear streets.

"We have the best snow plow ever invented — 500,000 pairs of feet walking through Times Square," Tim Tompkins said. "That’s been melting our snow."

As rain clouds cleared over in Madrid’s central Puerta del Sol square, around 50,000 people, many sporting large, brightly colored wigs, gathered to take part in Las Uvas, or The Grapes, a tradition in which people eat a grape for each of the 12 chimes of midnight. Chewing and swallowing the grapes to each tolling of a bell is supposed to bring good luck, while cheating is frowned upon and revelers believe it brings misfortune.

Police had painstakingly screened all those arriving to make sure drinks and bottles were left behind to avoid injury in the crowded square, so many quickly downed their sparkling cava wine before joining the animated party.

"It’s an annual tradition, and I’m here to make my wishes for the new year. If you eat the grapes your wishes will come true," beautician Anita Vargas said.

As the 12th grape was swallowed, the skies above most Spanish cities lit up with fireworks that slowly filled the air with smoke and the smell of gunpowder.

2010 was a grim year for the European Union, with Greece and Ireland needing bailouts and countries such as Spain and Portugal finding themselves in financial trouble as well.

"Before, we used to go out, celebrate in a restaurant, but the last two years we have had to stay at home," said Madrid florist Ernestina Blasco, whose husband, a construction worker, is out of work.

In Greece, thousands of people spent the last day of 2010 standing in line at tax offices to pay their road tax or sign up for tax amnesty.

"We can see that the quality of life is being degraded every day," Athens resident Giorgos Karantzos said. "What can I say? I don’t see the light at the end of the tunnel."

New Zealanders and South Pacific island nations were among the first to celebrate at midnight. In New Zealand’s Auckland, explosions of red, gold and white burst over the Sky Tower, while tens of thousands of people danced and sang in the streets below. In Christchurch, partyers shrugged off a minor earthquake that struck just before 10 p.m.

Multicolored starbusts and gigantic sparklers lit the midnight sky over Sydney Harbor in a pyrotechnics show witnessed by 1.5 million spectators.

"This has got to be the best place to be in the world tonight," Marc Wilson said.

Hundreds of thousands of people gathered along Hong Kong’s Victoria Harbor to watch fireworks explode from the roofs of 10 of the city’s most famous buildings.

In Vietnam’s capital, Hanoi, an estimated 55,000 people packed a square in front of the city’s elegant French colonial-style opera house for their first New Year’s countdown blowout, complete with dizzying strobe lights and thumping techno music spun by international DJs.

Vietnamese typically save their biggest celebrations for Tet, the lunar new year that begins on Feb. 3. But in recent years, Western influence has started seeping into Vietnamese culture among teens, who have no memory of war or poverty and are eager to find a new reason to party.

At Japan’s Zojoji temple in Tokyo, monks chanted and revelers marked the arrival of the new year by releasing silver balloons with notes inside. The temple’s giant 15-ton bell rang in the background.

In Seoul, South Korea, more than 80,000 people celebrated by watching a traditional bell ringing ceremony and fireworks, while North Korea on Saturday welcomed the new year with a push for better ties with its neighbor, warning that war "will bring nothing but a nuclear holocaust."

In Dubai, the world’s tallest building was awash in fireworks from the base to its needle-like spire nearly a half-mile (828 meters) above. Sparkling silver rays shot out from the Burj Khalifa in a 10-minute display.

In Rio de Janeiro, more than 2 million people gathered on Copacabana beach’s white sand for 20 minutes of fireworks, music and the unveiling of the logo for the 2016 Olympics. Traffic was shut down along the neighborhood’s main thoroughfares for much of the day in preparation for a party rivaled only by Carnival. Revelers drank and danced to samba played on stages along the 2.5-mile beach, and at midnight many waded into the water, jumping over seven waves for good luck.

In France, police were on alert for terror attacks and for celebrations getting out of hand. Rampaging youths typically set fire to scores of vehicles on New Year’s Eve. Interior Minister Brice Hortefeux said 53,820 police officers were mobilized, 6,000 more than usual.

France has been extra vigilant following threats from al-Qaida and the kidnapping of five French citizens in Niger.

Italians rang in the new year with illegal fireworks, shot off in squares and alleys — a tradition that usually results in numerous hand and eye injuries. Naples police Chief Santi Giuffre appealed to citizens to "give up or at least cut back on this" practice.

In central London, an estimated quarter-million revelers saw in the new year as red, white and blue fireworks — the colors of the Union Jack — shot from around the London Eye, lighting up the sky over the River Thames.

In Scotland, the four-day Hogmanay festival began Thursday night with a torch-lit procession through the streets of Edinburgh. Around 25,000 people took part, marching to the top of a hill to watch the burning of a model Viking ship. Hogmanay is derived from the winter solstice festival celebrated by the Vikings.

The Dutch celebrate by eating deep-fried dough balls covered in powdered sugar and washed down with champagne. The Danes jump off chairs to "leap into the new year." And the Austrians twirl in the new year with a waltz, carrying radios so they can dance to Strauss’ "Blue Danube" as the clock strikes midnight.

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Associated Press writers around the world contributed to this report.