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Authorities have attributed 14 U.S. deaths to the storm. Sandy killed 69 people in the Caribbean before making its way up the Atlantic.
Earlier Monday, the National Hurricane Center downgraded Sandy from a hurricane to a post-tropical storm, but said Sandy still packed a dangerous punch.
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New York Gov. Andrew Cuomo announced the closure of most major bridges in and out of Manhattan. Mass transit was completely shut down, and all of the East River crossings, including the Brooklyn, Manhattan, Williamsburg and Queensboro Bridges, were expected to close at 7 p.m.
The power was out for hundreds of thousands of New Yorkers and an estimated 5.7 million people altogether across the East.
Hundreds of thousands of people were under orders to flee the coast, including 375,000 in lower Manhattan and other parts of New York City. Some residents chose not to leave their homes.
"We're staying here. We have three children and our dog. Our dog is not going anywhere, so neither are we," said New York City resident Jolie Alony. "We have nowhere to go, so we're going to stay at home and we're going to ride the tide."
In Manhattan, a crane partially collapsed at 57th Street and 7th Avenue near Carnegie Hall. Authorities said they're concerned it may fall onto the street. Construction in New York has been suspended for the storm, so it was not immediately known if anyone would have been at the site. No injuries were reported. The luxury Parker Meridien hotel nearby was evacuated because of the crane.
Water also reportedly poured into the site of the World Trade Center.
About 90 miles off Cape Hatteras, N.C., the Coast Guard rescued 14 crew members by helicopter from the HMS Bounty, a replica 18th-century sailing ship that sank in the storm. The ship was built for the 1962 Marlon Brando film "Mutiny on the Bounty."
A missing crew member was found unresponsive off the North Carolina coast. She was later pronounced dead at the hospital. The search continued for the captain.
The New York Stock Exchange planned a rare shutdown for Monday and Tuesday because of Sandy. The last time the NYSE closed down for a weather-related event was on Sept. 27, 1985, for Hurricane Gloria.
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Sandy also caused a nightmare for travelers across the country. Thousands of flights were canceled, leaving people stranded at airports. According to the flight-tracking service FlightAware, 12,000 flights had been canceled for Monday and Tuesday.
President Barack Obama declared emergencies in Massachusetts, Connecticut, Rhode Island, New York, New Jersey and Pennsylvania, authorizing federal relief work to begin well ahead of time.
"When they tell you to evacuate, you need to evacuate," Mr. Obama said. "Don't delay, don't pause, don't question the instructions that are being given, because this is a powerful storm."
Mr. Obama said he was confident that local and federal governments had done all they could to prepare for the superstorm. He urged everyone to heed warnings from officials. The president canceled his campaign stop in Florida Monday morning to return to Washington and follow Sandy's progress.
The monster storm forced both the president and Republican presidential candidate Mitt Romney to change their campaign schedules in the last few days.
See photos of residents along the East Coast preparing for Sandy.
The Associated Press contributed to this report.
