SAN FRANCISCO—Hollywood’s big movie studios have succeeded in blocking software that would allow you to copy a movie onto your hard drive, but a court case beginning here today could overturn the restraining order, cracking the armor of an industry increasingly dependent on government protection.

At issue is a $50 software program called RealDVD, which enables users to copy a movie from a DVD onto their hard drives, creating a backup copy in case you break or lose the disc, or allowing you to tuck your DVDs away in the attic as many folks already do with the CDs they’ve ripped onto their hard drives.