In Australia, fireworks sprayed from the sails of the Sydney Opera House and the city's harbour bridge at midnight. Revellers in Dubai awaited what was supposed to be the world's largest fireworks show.
In Ukraine, anti-government protesters hoped to set their own record for the most people to sing a national anthem at the same time.
Revellers heading to New York City's Times Square could expect the annual ball drop but no mayor this year. The new year is to be rung in by US Supreme Court Justice Sonia Sotomayor instead.
Closer to the edge of the International Dateline, New Zealand bid farewell to 2013 with fireworks erupting from Auckland's Sky Tower as cheering crowds danced in the streets of the South Pacific island nation's largest city.
Known for glitz, glamour and over-the-top achievements like the world's tallest tower, Dubai hopes to break another record by creating the largest fireworks show ever.
Organisers plan to light up the city's coastline with a flying falcon made out of fireworks that will move across a massive man-made palm-shaped island alongside a countdown in fireworks. Organisers say they will also create a burst of light out of fireworks to imitate a sunrise and dazzle spectators with a United Arab Emirates flag that could also break records for being the largest ever made of fireworks.
The six-minute extravaganza will include 500,000 fireworks from 400 firing locations, all synchronised by 100 computers from stations across the city, said Barrett Wissman, co-chairman of IMG Artists that is managing the event. Guinness World Record officials will be on hand to measure the scale of the event.
Mr Wissman said the display will cover 30 miles (48km) of seafront. "It is really mind-blowing, the size of this," he added.
In Sydney, organisers had expected to set off seven metric tons of pyrotechnics in 12 seconds. The estimate appeared accurate. "It filled up the whole sky," said Mona Rucek, a 28-year-old tourist from Munich, Germany.
In Tokyo, five priests at the Zojoji temple used ropes to swing a wooden pole against a large bell, sounding the first of 108 gongs to mark the new year. Simultaneously, "2014" lit up in white lights on the modern Tokyo Tower in the background.
Both Japanese and tourists jammed the temple grounds for the traditional ceremony. Suburban resident Juji Muto said he was curious to hear how the bell sounded. At his age, the 75-year-old pensioner said he wishes, as every year, for good health in the new year.
China planned light shows at part of the Great Wall near Beijing and at the Bund waterfront in Shanghai. The city of Wuhan in central Hubei province called off its fireworks show and banned fireworks downtown to avoid worsening its smog.
Pope Francis used his year-end prayer service of thanksgiving to urge people to ask themselves: Did they spend 2013 to further their own interests or to help others?
In his homily, the pontiff asked people to reflect if they used 2013 to make the places where they live more live-able and welcoming. Citing Rome as an example, Francis said the city is full of tourists, but also refugees.
Britain planned to welcome 2014 with a mixture of futuristic fireworks and torch-lit tradition. The main Hogmanay event in Scotland is being held in Edinburgh.
At Berlin's Brandenburg Gate, hundreds of thousands of people were starting to assemble for what organisers say is one of the world's biggest outdoors New Year's Eve party, a traditional German gathering featuring jelly doughnuts and sparkling wine.
More than 260 people had been injured by firecracker blasts and celebratory gunfire in the Philippines ahead of New Year's Eve celebrations.
Department of Health spokesman Dr Eric Tayag said he expected the number of injuries to rise sharply as Filipinos commemorate the end of a year marked by tragic disasters, including a November 8 typhoon that left more than 6,100 dead and nearly 1,800 missing.
"Many here are welcoming the new year after losing their mothers, fathers, siblings and children so you can imagine how it feels," said village chief Maria Rosario Bactol of Anibong community in Tacloban, the city worst hit by Typhoon Haiyan. "I tell them to face the reality, to move on and stand up, but I know it will never be easy."
In Hong Kong, pyrotechnics were fired near the Kowloon peninsula and from the tops of seven skyscrapers. A British colonial-era canon was fired at midnight in a tradition dating from the end of the Second World War.
New Year's celebrations in Indonesia were widespread except in the city of Banda Aceh where Islamic clerics prohibit Muslims from celebrating New Year's Eve.
In New York City, outgoing Mayor Michael Bloomberg, who hobnobbed with celebrities during past Times Square celebrations, is sitting out this year's festivities to spend time with family and friends. Mayor-elect Bill de Blasio will be sworn in at one minute past midnight at his Brooklyn home.
Justice Sotomayor, a New York City native, will lead the final 60-second countdown and push the ceremonial button to signal the descent of the Times Square New Year's Eve ball in front of an estimated one million revellers.