At the Microsoft pre-E3 press conference, the company kicked off their program with information about the Xbox 360 and the Xbox Live Gold program. Most importantly, they mentioned that the Gold membership was getting a bit of an upgrade.
Xbox Gold membership will indeed transfer over to the Xbox One, so you will not have to resubscribe or subscribe to a brand new membership if you purchase the new console.
In addition, as of July 1st, all Gold members will receive two free game downloads that are yours to keep no matter what. This perk goes to both new and current members. The games are actually quite substantial, but I have a feeling many people already own them who want them—Assassin's Creed 2 and Halo 3.