For the noun referring to a horizontal level of a building, story is the standard spelling in American English, and storey is preferred in all the other main varieties of English. The plural of the American story is stories, and the plural of the storey is storeys.
Of course, English speakers everywhere use story for an account of a series of events and related definitions.
The building will stand four stories tall along Franklin Street. [Chapel Hill News]
An eight-story retail space would adjoin the East Tower, and a below-ground, four-story parking garage would offer 850 parking spots. [Boston Globe]
Outside the U.S.
The announcement of the seven-storey, 48-unit building was made Tuesday morning at the Winnipeg Chinese Cultural and Community Centre. [Winnipeg Sun]
The next plan for the area, a proposed 50-storey skyscraper called the Shanghai Tower, simply fills her with dread. [The Guardian]
Firefighters were called to the two-storey brick and concrete house, on State Highway 23 at Whatawhata, just before 1pm. [Stuff.co.nz]