Flood alerts have been issued for most of Scotland, with the risks heightened because further torrential downpours today will fall on already water-logged ground following a day of rain yesterday.
Seven people, including four children, were last night airlifted to safety by a Royal Navy helicopter after being trapped for six hours by flood waters at a farm near Closeburn, Dumfries and Galloway.
About 40 homes were evacuated in the village of Kirkconnel, Dumfries and Galloway, while firefighters helped rescue more than 14 people from flooded properties in New Cumnock, Ayrshire.
However, weather forecasters are predicting Scotland's Hogmanay parties will beat the weather. They are expecting more settled conditions, with evening temperatures in Edinburgh, where most of the crowds will gather at the famous street party, to be a mild 5°C.
"For the evening the driest in the UK will be across Scotland," said Helen Chivers, of the Met Office.
The Scottish Environment Protection Agency had 32 flood warnings in place last night as the heavy rain caused major flooding on some roads that led to widespread disruption.
Families in the St Conal's area of Kirkconnel were being hosted at the Miners Hall, which had been turned into a temporary rest centre.
Closures on roads included the A74(M), the A76 and the M77, while flooding also disrupted the rail network. Rail users faced delays between Queen Street, Glasgow, and Edinburgh due to flooding at Linlithgow, while there were delays of up to an hour between Glasgow Central and Edinburgh.
Virgin Trains said there were no services between Carlisle and Carstairs, due to flooding between Lockerbie and Carstairs. Trains from London Euston to Glasgow and Edinburgh were also disrupted.
Rivers that burst banks included the Nith, causing flooding in the Whitesands area in Dumfries. Police said road closures in the town had caused traffic to become gridlocked.
In the village of Carsphairn, also Dumfries and Galloway, residents described the conditions as some of the worst they had experienced in 40 years.
Police said the village of Moniaive was almost cut off at one point due to flooding on the A702, and a family had to be evacuated from a bungalow. Firefighters used rescue boats to evacuate people.
The emergency services also helped residents hit by flooding in the coastal village of Port Logan, Rhins of Galloway.
Water levels were being closely monitored on a number of other rivers in the region, including the Cree in Newton Stewart.
There were also a series of other road closures in the region.
In Dundee, residents were evacuated from a number of properties after torrential rain caused a wall to collapse and a landslide. Nobody was hurt.
Revellers started the Hogmanay celebrations last night with the annual torchlit procession through Edinburgh. Led by Shetland's Up Helly Aa Vikings accompanied by their pipes and drums, the event culminated in a spectacular Son et Lumiere and fireworks display.
About 80,000 people are expected in the capital for its famous Hogmanay street party, which will bring in 2014.
The Pet Shop Boys will headline a Concert In The Gardens, while the street party will have music on three stages. Traditional Scottish music will be playing at The Keilidh, an outdoor dance event.
Ms Chivers added: "In Edinburgh there is a very small chance of a shower in the early evening but the rest of the evening looks dry."