In Glasgow, 1.4in (35mm) of rain fell last night, making it the wettest place in Scotland.
Some residents had to be evacuated from their homes after flooding in Greenock, Dumbarton and Carluke.
A number of roads were closed and trains between Greenock and Wemyss Bay were cancelled.
The main road between Port Glasgow and Greenock was closed and some motorists had to be rescued from their cars.
Residents in Inverclyde described it as the "worst flooding" they had ever experienced in the area.
Motorists were warned to take care on roads across Renfrew-shire, Lanarkshire and Ayrshire affected by severe localised flooding.
The A814 was shut both ways between Renton Road in Dumbarton and Red Road in Cardross and the M9 was closed in both directions at junction 10.
The River Endrick burst its banks close to the Drymen Bridge, flooding the A811 and closing it completely.
The A8 was closed between Newark Roundabout, Port Glasgow, and Dellingburn Street, Greenock.
No trains were stopping at Dumbarton East, there were no services to and from Wemyss Bay, and no trains between Glasgow Central and Gourock. Trains were beginning and ending their journeys at Port Glasgow.
The Met Office has issued amber weather warnings for Strathclyde, Central Scotland, Tayside, Fife, the south-west and Lothian and Borders areas.
A spokesman said the persistent rain would "last well into the day" and added: "This will fall on to already saturated ground, leading to the risk of flooding and travel disruption.
"The rain will be accompanied by strengthening southerly winds, with severe gales likely in the south-west."
One Inverclyde resident said: "When I left this morning there were no roads going out of Greenock. Shore Street was the worst I've ever seen it in my life. It was impassable in one lane.
"In Elder Street in Battery Park I had to drive on the other side of the road.
"The police stopped me in Port Glasgow and said the rest of the Inverclyde roads were closed.
"HGVs were being diverted. There was about 15 of them all parked off the main road."
Meteorologist Brendan Jones said the rain was caused by mild winds coming off the Atlantic bringing of moisture in their wake.
He said Scotland should expect worsening weather in the coming week, predicting winds of between 75mph and 80mph in the north.