At the recent State of the Net conference, Tom Tauke, Verizon's Executive Vice President, told participants that Verizon did not intend to filter the Internet to enforce copyright compliance.
Here's an excerpt from "Verizon: No Thank You on Copyright Filtering":
He [Tauke] said that it would be 1) a bad business decision "to assume the role of being police on the Internet;" 2) a likely invasion of privacy; and 3) would open the door to requests from others to filter out other objectionable material, like indecency and online gambling.
Read more about it at "Verizon: We Don't Want to Play Copyright Cop on Our Network."