Imagine two objects with equal mass in empty space attracting each other. One of these objects moves tangentially with a very high speed (lets say 0.9c). (p1 = (0, 0) p2 = (1, 0) v1 = (0, 0) v2 = (0, 0.9c)). Would the direction of the force, acting on the resting mass point directly towards the other mass, or to a point, where the moving mass was some time ago. Einstein says, that information cant travel faster than light, so whats about gravity? Does the gravitational pull really point towards the center of mass, even if it its moving?
Gravity, like all cause-effect relationships, propagates at a maximum speed of $c$; indeed from the Einstein field equations small amplitude (linear limit) gravitational waves travel at precisely $c$.
A good idea for what is going on comes from an approximation of General Relativity called Gravitoelectromagnetism. This makes an approximate analogy between gravity and electrodynamics as the approximation has the same form as Maxwell's Equations. In electrodynamics, charges influence one another through retarded potentials as described by the Liénard-Weichert potentials and Feynman's delayed force formula; see the Physics SE Question "Do electrostatic fields really obey “action at a distance”? for more details. The force on a charge by another is roughly that calculated from the position of the latter at a time $d/c$ before the present, where $d$ is the distance separating the charges.
The same is true for gravity. But be careful of pushing the purely "delayed force" idea too far: it's not the whole picture, either in electrodynamics or gravitation. In particular, the great Laplace tried to formulate a theory of gravitation with delayed forces and found that it foretold grossly unstable planetary orbits. Gravitoelectromagnetism introduces the delay in a Lorentz covariant way and gets rid of the instability (well, at least enough to make it in keeping with physical observations). But, as we have noted, even gravitoelectromagnetism is a linearized approximation to the Einstein field equations.