What would be the dynamics of a double-planet system, similar to Earth / Moon, but with both bodies nearly Earth-sized? Researching a sci-fi story involving a "twin-planet" system. Is such an arrangement (however unlikely) physically possible? And if so, must they be tidally locked with each other, similar to the Moon, month-long days, etc?  (or good reference sources for a layman?)
 A: I see no reason why it should be impossible. A binary planet system should exist in a reasonably stable orbital configuration.
As Javier pointed out, Pluto and Charon are similar in size and mass, like a small-scale version of what you describe. The important thing to note here is that the barycenter of the Pluto-Charon system is outside either planet. In most systems (e.g. Earth-Sun, Jupiter-moons of Jupiter, etc.), the barycenter is inside one of the bodies (generally the more massive one). In the system you describe, the barycenter would be exactly in the middle of the system.
Pluto and Charon show that it is possible for two small bodies to exist in this arrangement. Certain binary star systems show the same characteristics: the barycenter is outside both bodies. This can thus happen on small and large scales; it seems likely it could happen somewhere in between.
I should add that I'm not quite sure how something like this could form. The bodies would have to form in just the right places, at just the right times.
