An estimated 50 million people could be affected, with up to one million ordered to evacuate homes.
At least five million people across several states are without electricity.
The full extent of the damage may not be known until daybreak.
Over the past week Sandy has killed dozens of people as it carved a path of destruction through the Caribbean.
Public transport has been halted in several eastern US cities, and thousands of flights have been grounded.
Continue reading the main story
Start Quote
The New York City subway system is 108 years old, but it has never faced a disaster as devastating as what we experienced last night”
New York City transport director Joseph Lhota
In other developments:
More than 200 patients were evacuated from New York University's Tisch Hospital after its power went out and a backup generator failed.
America's oldest nuclear power plant, Oyster Creek in New Jersey, was put on alert due to rising water, the Nuclear Regulatory Commission said.
The New York Stock Exchange will stay shut on Tuesday - the first time it has closed for two consecutive days due to weather since 1888.
A crew member from a replica of HMS Bounty has died and the captain is missing after the ship sank in mountainous seas off North Carolina on Monday.
Both President Barack Obama and Republican challenger Mitt Romney cancelled campaign appearances little more than a week before the presidential election.
The storm made landfall close to Atlantic City in New Jersey at about 20:00 local time (midnight GMT), packing winds of more than 80mph (129km/h).
Much of Atlantic City is under water, and 30,000 residents were evacuated.
'Lower Manhattan covered'
Sandy threatens an 800-mile (1,290-km) swathe of the US, from the Atlantic Ocean to the Great Lakes in the Mid-West.
It lost its hurricane status late on Monday as it neared the coast and collided with winter weather systems, but was still packing hurricane-strength winds.
Continue reading the main story
The greatest storms on Earth
A tropical storm is classified as a hurricane when wind speeds reach 74mph
A hurricane can expend as much energy as 10,000 nuclear bombs over its lifecycle
The hurricane's spiral is due to the Coriolis Effect, which is generated by the Earth's rotation
What are the ingredients for a perfect storm?
Just before 02:00 EDT (06:00 GMT) the National Hurricane Center placed the centre of Sandy just south of Lancaster, Pennsylvania.
In New York, some 375,000 residents were ordered out of Lower Manhattan and other areas, as the Hudson and East rivers began overflowing.
A record storm surge of 13.7ft (4.15m) swept into Lower Manhattan, flooding seven major subway tunnels.
"The New York City subway system is 108 years old, but it has never faced a disaster as devastating as what we experienced last night," city transport director Joseph Lhota said early Tuesday.
"Lower Manhattan is being covered by seawater," Howard Glaser, director of operations for the New York state government, was quoted as saying. "I am not exaggerating. Seawater is rushing into the Battery Tunnel."
Battery Tunnel links Manhattan with Long Island.
The city's Consolidated Edison utility provider said some 500,000 homes in Manhattan were without power.
There were reports of an explosion at a Con Edison power station on the east side of Manhattan.
Vice president John Miksad said it was caused by flooding or flying debris, and he added it could take a week to restore power completely.
New York Mayor Michael Bloomberg said the storm surge was higher than the highest forecast, but he expected the waters to start receding from midnight local time.
Nasa released time-lapse animation of the hurricane from Space - courtesy Nasa GOES Project
Elsewhere in the city, the storm left a construction crane bent double next to a skyscraper and caused the facade off a four-storey building to collapse.
The UN headquarters in New York is also to stay closed.
Officials reported at least 12 deaths in New Jersey, New York, Maryland, West Virginia, Pennsylvania and Connecticut - several due to fallen trees.
In addition to the US deaths, a Canadian woman was reported killed by flying debris in Toronto.
Forecasters have said Sandy could linger over as many as 12 states for 24-36 hours.
President Obama declared emergencies in Massachusetts, Connecticut, Rhode Island, New York, New Jersey and Pennsylvania.
In Washington DC, federal government offices are closed until Wednesday.
Public transport was suspended in the US capital, New York, Baltimore, Philadelphia and Boston.
Amtrak has suspended passenger train services across the north-east, while nearly 14,000 flights were cancelled, according to Flightaware.com.
Up to 3ft (91cm) of snow is expected to fall on the Appalachian mountains in West Virginia, Virginia and Kentucky.
The disaster estimating firm Eqecat has forecast that Sandy could cause economic losses to the US of between $10bn and $20bn (£6.2bn-£12.4bn).
