For years, cable companies and other pay-television providers have fretted about the threat that online-video subscription services like Netflix Inc.'s could pose to their business. Now, one of those providers is plunging into Web streaming.

Telecom giant Verizon Communications Inc. and Coinstar Inc., the operator of Redbox DVD-rental kiosks, plan to start offering a national subscription service later this year that would offer Internet access to a selection of movies and other content. The service will pair online access...