At the Vatican, Pope Benedict XVI celebrated New Year's Eve with a vespers service in St. Peter's Basilica, giving thanks for 2012 and look ahead to 2013, the British publication The Guardian reported.
In his sermon, the pontiff said sometimes it's difficult to remember that good prevails when bad news death, violence and injustice "makes more noise than good."
Taking time to meditate and pray can "find healing from the inevitable wounds of daily life," he said.
Even Myanmar, formerly Burma, which had banned large public gatherings when it was under military rule, was celebrating, witnesses said. Thousands of spectators were expected to view a fireworks display and watch entertainers in Yangon, formerly Rangoon.
The mood was subdued in New Delhi after last week's death of a 23-year-old victim of a gang rape. The army canceled its celebrations, as have the governments in the states of Punjab and Haryana, residents and nightclubs, the BBC said.
As U.S. congressional leaders worked to avert the pending fiscal cliff -- a confluence of tax hikes and spending cuts set to take place Tuesday if nothing happens -- President Obama commented he was spending New Year's Eve in Washington.
Obama, during a public statement about fiscal cliff negotiations, declined an offer to go to someone's house, saying, "I don't want to spoil the party."
In the United States, Rasmussen Reports said 65 percent of adults indicated they'd be awake at midnight to greet 2013.
At least 60 percent said they would be "somewhat likely" to watch the traditional ball-drop in New York's Time Square, the report indicated.
The nationwide survey of 1,000 adults was conducted Dec. 22 and has a margin of error of 3 percentage points.