More than 100 emergency calls were made in just over six hours on Saturday night.
One councillor in the north-west said the downpour was “apocalyptic”.
The Met Office issued a yellow weather warning for rain on Saturday evening as a week that began with the top temperatures of the year so far ended in a washout.
In parts of Derry and Strabane, Co Tyrone, police issued warnings about hazardous driving conditions.
Flooding was reported in several areas of Derry city, including the Strand Road and Foyle Road.
A spokesperson for the Northern Ireland Fire & Rescue Service (NIFRS) said today: “Between 7.04pm on Saturday and 1.30am on Sunday, NIFRS received a total of 106 emergency 999 flood-related calls which resulted in our firefighters responding to 49 operational incidents.
“NIFRS rescued one person from a vehicle in water and five persons trapped within flooded properties.
“NIFRS maintained normal emergency response throughout the evening, attending a range of operational incidents including special service calls and other emergencies.”
SDLP councillor Steven Edwards said Castlederg in Tyrone was particularly badly hit.
He added: “I’ve visited and spoken to a number of homeowners and businesses across the 'Derg who’ve been impacted by flooding.
"Apocalyptic levels of rain and surface water for many. My heart goes out to them all.
“I would advise anyone impacted by flooding to document what they can as this may prove vital further down the line in terms of claims and compensation.”
Anoop Guram, whose takeaway business in Strabane was flooded, told the BBC the water was about three inches deep in his premises.
"We had to close... there will be damage to the floors,” he said. "I will have to get the loss adjusters. You're talking about £12,000 or £15,000 in [damages] total."