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Einstein's theory of general relativity predicts that the only stationary configuration of an isolated black hole is the Kerr spacetime, which has a unique multipolar structure and a spherical shape when non-spinning. This is in striking contrast to the case of other self-gravitating objects, which instead can in principle have arbitrary deformations even in the static case. Here we develop a general perturbative framework to construct stationary stars with small axisymmetric deformations, and study explicitly compact stars with an intrinsic quadrupole moment. The latter can be sustained, for instance, by crust stresses or strong magnetic fields. While our framework is general, we focus on quadrupolar deformations of neutron stars induced by an anisotropic crust, which continuously connect to spherical neutron stars in the isotropic limit. Deformed neutron stars might provide a more accurate description for stellar remnants formed in supernovae and in binary mergers, and can be used to improve constraints on the neutron-star equation of state through gravitational-wave detections and through the observation of low-mass X-ray binaries. We argue that, if the (dimensionless) intrinsic quadrupole moment is of a few percent or higher, the effect of the deformation is stronger than that of tidal interactions in coalescing neutron-star binaries, and might also significantly affect the electromagnetic signal from accreting neutron stars.