The anisotropic interaction of the electric field vector of intense laser radiation with the dipole moment induced in a polarizable molecule by the laser field creates aligned pendular states. These are directional superpositions of field-free states, governed by a cos(2) theta potential (with theta the angle between the molecular axis and the field vector). We show that the spatial alignment and other eigenproperties can be derived from spheroidal wave functions, give explicit expressions for low- and high-field limits, contrast the induced pendular states with those for permanent dipoles subject to static fields, and present calculations demonstrating the utility of the induced states for rotational spectroscopy, laser alignment, and spatial trapping of molecules.