MAYFIELD VILLAGE, Ohio—In a lab at Progressive Corp. ’s suburban headquarters, managers and technicians at the auto-insurance giant watch a colleague drive from his home outside Cleveland to the city zoo. A dot on a computer screen moves along a map overlaid with speed limits, turning red when the driver is speeding.

The demonstration is part of an effort to figure out how location data could someday be used to assess drivers, as the roughly $185 billion auto-insurance industry undergoes a wholesale change in how companies size up risk. Using devices installed in customers’ cars, Progressive and other auto insurers are tracking things like how far their customers drive and how often they slam on the brakes.

For decades, insurers have relied heavily on lumping applicants into broad actuarial categories by characteristics such as age, gender and car type to supplement information gathered from driving records. Now, they are collecting reams of personal data in hopes of drawing much more tailored conclusions.

The catch is the industry needs its customers’ consent to gather the information, and many customers are wary.

“I know some people say, ‘What do you have to hide,’ but I don’t want big business or Big Brother being involved in my personal life,” says Shauna Aiken, a San Diego driver of a Mazda Miata. “It just creeps me out.”