Northern is warning people not to travel today and says it does not know when services will resume.
It said disruption is expected to continue until the end of the day and adds that there are no bus replacement services being offered.
The rail company is urging passengers not to visit stations but to stay at home until further notice.
All services have been terminated at stations in Lancashire, Greater Manchester, Cumbria, Merseyside and Cheshire.
A Northern spokesman said: "Due to the severe weather and numerous incidents caused by Storm Franklin, we will be terminating all services in the North West.
"No further trains until at least 10.30am, and this might be extended.
"Customers are strongly advised not to travel today due to widespread disruption across the network.
"Please, do not attempt to travel and do not head to stations as there are no alternatives."
A number of trees have fallen onto tracks in Greater Manchester and Cheshire, blocking the railway at Rose Hill Marple, Gatley and Macclesfield.
Services are also unable to run between Workington and Carlisle due to flooding on the railway at Aspatria.
Northern said unused tickets may be used on Northern services until the end of Tuesday (February 22).
You can find the latest traffic, travel and weather updates throughout the day on our live blog.