When people talk about prolific, successful engines, the first port of call will likely be the Unreal Engine. It's come to the point where it's easy to be genuinely surprised by the realization that you're playing an Unreal game. There's another engine that's powered some of the highest rated games of all time though, and it may already have gotten a next-gen upgrade.
The Source Engine has powered Half-Life 2, Left4Dead, Portal and countless other games, mods and user-created content, and has been in use for over a decade. No doubt there have been countless upgrades to the engine to allow developers easier creative freedom, but a bigger update will definitely be shown over the next few years, hopefully sooner rather than later.
People going through the code for the newly released Source Filmmaker have found reference to the Source Engine 2, as well as icons hidden for "Source 2 Tools." It's good news for Half-Life 3 fans, who now have a new thing to blame the game's disappearance on: "they're building it in the new engine, OF COURSE!"