In Belgium, around 10 houses collapsed in Pepinster after the river Vesdre flooded the eastern town and residents were evacuated from more than 1,000 homes.
The rain has also caused severe disruption to public transport, with high-speed Thalys train services to Germany cancelled. Traffic on the river Meuse is also suspended as the major Belgian waterway threatens to breach its banks.
Downstream in the Netherlands, flooding rivers damaged many houses in the southern province of Limburg, where several care homes were evacuated.
In addition to the eight who died in the Euskirchen region, another seven people died elsewhere in North Rhine-Westphalia, several of them in flooded cellars, as well as two firefighters.
"It's a catastrophe! There are dead, missing and many people still in danger. All of our emergency services are in action round the clock and risking their own lives," said Malu Dreyer, premier of the Rhineland-Palatinate.
Further down the Rhine river, the heaviest rainfall ever measured over 24 hours caused flooding in cities including Cologne and Hagen, while in Leverkusen 400 people had to be evacuated from a hospital.
In Wuppertal, known for its overhead railway, locals said their cellars had been flooded and power cut off.
The Greens, running second in opinion polls ahead of Germany's federal election in September, blamed the floods on global warming.
"This is already the impact of the climate catastrophe and this is another wake-up call to make us realise: this is already here," Katrin Goering-Eckardt, the parliamentary leader of the Greens, told RTL/NTV television.
Weather experts said that rains in the region over the past 24 hours had been unprecedented, as a near-stationary low-pressure weather system caused sustained local downpours also to the west in France, Belgium and the Netherlands.
Rainwater draining into the Rhine, where shipping traffic was partly suspended, was expected to test flood defences along the river, including in Cologne, on the lower Rhine, and Koblenz, where the Rhine and Moselle merge.
More heavy rain was due in southwestern Germany, on the upper reaches of the German Rhine, later on Thursday and Friday, the German Weather Service said.