The National Weather Service predicted that rain totals could hit 15 inches in some places by Monday afternoon.
"Yesterday, 3.77 inches of rain fell in Boston, shattering an old record, so that just gives you an idea of how heavy the rain has been," says CBS News meteorologist George Cullen, adding that showers could last into Wednesday.
In the Merrimack Valley, north of Boston on the New Hampshire line, the Merrimack and Spicket rivers overflowed their banks and forced the evacuations of hundreds of people.
All residents could do is watch as water pushed its way through towns, forcing its way into homes any way it could, reports CBS News correspondent Sharyn Alfonsi.
Firefighters warned roommates Erica Digaetano, 22, and Kelly Malynn, 23, to leave their first-floor apartment in downtown Haverhill. Water had filled the basement up to the ceiling and was still rising.
"My landlord has an office under here and everything is just floating in it," Digaetano said.
Tens of millions of gallons of sewage spilled the Merrimack River after pipes burst in Haverhill on Sunday, and millions more poured from a treatment plant in Lawrence after floodwaters knocked it out of service Monday, reports CBS News' Cheryl Casone.
"The mix is 90 percent storm water, 10 percent sewage, right now about 50 million gallons per day" was ending up in the overflowing Merrimac River, said Haverhill Sewage Treatment Plant acting director Bob Ward.
"It's going to get worse before it gets better," Massachusetts Gov. Mitt Romney said.
Emergency crews took to flooded streets in boats and used bullhorns to urge people to leave their homes in Lowell. Forecasters said the river could rise past 60 feet by Monday night, putting it at more than 8 feet over flood stage.
In Wakefield, Mass., about 15 miles north of Boston, Ralph Tucci watched nervously as shallow water in the front yard lapped near his front door.
"That's what I have left — just six more inches," said Tucci, 50, who spent $247 on a pump Monday to try to protect his home. "The only thing I've got to do now is buy a boat," he joked.
Four-wheel drives have been used to get people out of their homes in Peabody, Mass., reports Carl Stevens of CBS Radio station WBZ-AM. Much of the downtown area is underwater.
In New Hampshire, more than 600 roads were damaged, destroyed or under water. Gov. John Lynch said his own front yard in Hopkinton had become a pond. In Concord, flooding closed St. Paul's School and the prep school was working to get its students back home on short notice.
Flooding knocked out the school's heating plant and sewage pumping station and hit some dorms, the library, the health center, post office and performing arts center at St. Paul's, which has students from around the world.
Dan Burke, who owns a backhoe, helped people in Rochester, N.H., get prescriptions and retrieve belongings from their homes after the city ordered the evacuation of nearly 2,000 homes downstream from a dam that appeared to be in danger.
"We're just trying to help people get out, trying to get them at least on their way, so they don't have to lose everything," Burke said.
In southern Maine, fast-rising floodwaters forced scores of families to flee homes near the Mousam River. Kayakers paddled down a main street in York Beach, where firefighters in a boat went building to building to make sure that propane tanks were shut off.
Former President George Bush and his wife arrived at their summer home in Kennebunkport, Maine, over the weekend, but the house was unaffected, said Jean Becker, Bush's chief of staff.