The Supremes rule unanimously in favor of MGM, saying:

We hold that one who distributes a device with the object of promoting its use to infringe copyright, as shown by clear expression or other affirmative steps taken to foster infringement, is liable for the resulting acts of infringement by third parties.

As many people are noting, this isn't as bad as it sounds. P2P apps are safe as long as their parent companies aren't found to have actively induced infringement. Also, remember that this wasn't the test that the entertainment industry wanted, they had argued that an active inducement test wouldn't be sufficient and wanted the test to involve the extent to which a device was being used for infringement. Gigi Sohn of Public Knowledge spins this pretty strongly as at least a partial victory:

What this means is, in the absence of such clear expression or other affirmative acts fostering infringement, a company that provides peer-to-peer technology is not going to be secondarily liable under the Copyright Act.