The stability of planetary orbits in binary systems is explored, with emphasis on the inclinations of the relevant orbit planes and associated time scales. If the planetary orbit has high inclination relative to the orbital plane of the binary, the so-called Kozai mechanism causes large variations in the eccentricity and inclination of the planet' s orbit. In the point mass model, the amplitude of this phenomenon is independent of the semimajor axis of the binary or the proximity of the planet, while the time scale depends on those quantities. The dynamical interaction of several planets in the system, or, more generally, any additional effect that causes extra precession of the pericenter, can enhance stability by suppressing the mechanism. As an illustrative example, we study the stability of the Solar System under the action of a hypothetical, distant, high-inclination companion star. From this example, there emerges a new result: as long as the eccentricities remain small, the Solar System mimics a rather "rigid" disk in the sense that all the planetary orbital planes move in concert, with small mutual inclinations. This is due to the collective, dynamical interaction of the planets and does not occur if planetary masses are negligible.