WASHINGTON—The National Security Agency's monitoring of Americans includes customer records from the three major phone networks as well as emails and Web searches, and the agency also has cataloged credit-card transactions, said people familiar with the agency's activities.

The disclosure this week of an order by a secret U.S. court for Verizon Communications Inc.'s phone records set off the latest public discussion of the program. But people familiar with the NSA's operations said the initiative also encompasses phone-call...