Rising water from the river also forced the evacuation of a downtown hospital.
Officials say 176 patients are being evacuated from Mercy Medical Center, including its nursing home facility. Patients started being taken to other hospitals in the region late Thursday night. The evacuation was continuing Friday morning.
Officials estimated that 100 blocks were underwater in Cedar Rapids, reports CBS News correspondent Dean Reynolds, where several days of preparation could not hold back the rain-swollen river. Rescuers had to use boats to reach many stranded residents, and people could be seen dragging suitcases up closed highway exit ramps to escape the water.
"We're just kind of at God's mercy right now, so hopefully people that never prayed before this, it might be a good time to start," Linn County Sheriff Don Zeller said. "We're going to need a lot of prayers and people are going to need a lot of patience and understanding."
Days of heavy rain across the state have sent nine rivers across Iowa at or above historic flood levels. Residents were already steeling themselves for floods before storms late Wednesday and early Thursday brought up to 5 inches of rain across west central Iowa.
And nearly every town on the Mississippi River from Northern Iowa to Southern Missouri has been alerted that the river is at or above flood stage and is posing the worst threat in 15 years, reports Reynolds.
"We are seeing a historic hydrological event taking place with unprecedented river levels occurring," said Brian Pierce, a meteorologist with the National Weather Service in Davenport. "We're in uncharted territory - this is an event beyond what anybody could even imagine."
Gov. Chet Culver has declared 55 of the state's 99 counties as state disaster areas.
No deaths or serious injuries were reported in Iowa, but one man was killed in southern Minnesota after his car plunged from a washed-out road into floodwaters. Another person was rescued from a nearby vehicle in the town of Albert Lea.
In Des Moines, officials said they were urging residents to evacuate more than 200 homes north of downtown because of concerns that the Des Moines River would top a nearby levee. Some residents also were ordered to evacuate homes along rivers in Iowa City and Coralville.
In Cedar Rapids, a city of about 124,000, flood waters downtown neared the top of stop signs and cars were nearly covered in water. It wasn't clear just how high the river had risen because a flood gauge was swept away by the swirling water.
"It's going door to door to make sure people don't need to be rescued, cause right now they can't get out on their own," said Dave Koch, a spokesman for the Cedar Rapids Fire Department. "It's just too deep."
The surging river caused part of a railroad bridge and about 20 hopper cars loaded with rocks to collapse into the river. The cars had been positioned on the bridge in hopes of weighing it down against the rising water.
"I've never seen anything close to this," Firefighter Mike Cheney told Reynolds. "It's gonna be years before things get back to normal."
Joe Childers, an official at a U.S. Bank in downtown Cedar Rapids, was in jeans and tennis shoes as he worked to move documents and other items upstairs or out of the building.
"We're trying to keep water out of as many places as we can," he said. "It's pretty amazing. I don't think anyone really expected it this far."
Prisoners had to be moved from the Linn County jail, including some inmates who had been transferred from the Benton County jail in Vinton because of flooding. The sheriff's office also was under water, Zeller said.
"We've had to move our operations out of the area and to our alternate emergency site," Zeller said. "We are just trying to regroup. When you don't have all of your equipment and you don't have all your facilities to operate out of - we're at a little bit of a disadvantage ... but we're carrying on as normal."
Several emergency shelters were opened, and the city had closed all but one of its bridges over the Cedar River.
"I believe that this is God's way of doing things, and I've got insurance, so I'm not worried about it," said Tim Grimm, who was forced to leave his home in the city's Czech Village area.
In Austin, Minn., the Cedar River was expected to crest Thursday night at 22 feet, 7 feet above flood stage. The river reached 25 feet in a 2004 flood that caused major damage in the city.
Some businesses and offices were closed because of the flooding, including a Hormel Foods corporate office and its Spam Museum. The city of Austin, however, has bought many properties in the flood plain since the 2004 flood and tore structures down.
"The city has been very proactive and that's going to save them some problems this time," said Mike Welvaert, a weather service meteorologist.
Flooding this week also caused damage across southern Wisconsin, where thunderstorms continued pounding the area on Thursday.
A funnel cloud was reported in Grant County in southwestern Wisconsin, said Chris Kuhlman, a weather service meteorologist. The weather service also said flash floods in the county closed two highways and required rescues, though a sheriff's office dispatcher did not immediately have those details.
Just southeast of Grand Rapids, Mich., crews pulled the body of a motorist from a car found drifting in the swollen Thornapple River. State police said they believe the 57-year-old man called on his cell phone but didn't say what happened or where he was; they found him using global positioning equipment.
People in several northern Missouri communities, meanwhile, were piling up sandbags to prepare for flooding in the Missouri River, expected to crest over the weekend, and a more significant rise in the Mississippi River expected Wednesday.