In this thesis we present exact solutions of geometrical theories of gravity, i.e. those of a general relativistic type. In chapter 1, we give a short introduction into the calculus of exterior differential forms, introduce the Cotton 2-form, and investigate its properties (irreducible decomposition, number of independent components, conformal transformation, classification in three dimensions, analytic properties). In view of covariantly conserved quantities, we investigate the relation between the Cotton 2-form, the Bach 3-form, and the Chevreton tensor (a superenergy tensor of the electromagnetic field). Chapter 2 is devoted to gravity in three dimensions. For a model of Mielke and Baekler (MB), we find an exact BTZ-like solution with constant axial torsion. We determine its autoparallels, extremals, Killing vectors, and global charges. Furthermore, we derive from the MB-model a teleparallelism model, Einstein-Cartan theory, and topologically massive gravity. We show how the BTZ-solution with torsion reduces to solutions of the aforementioned subcases. In conclusion we construct a new perfect fluid solution of Einstein's field equation in three dimensions. In the last chapter we turn to four-dimensional metric-affine gravity. We devise a model which allows for the breaking of Lorentz invariance by means of a vector-like quantity (aether). Therefore we take a vector-piece of the nonmetricity. We set up a Lagrangian and derive the field equations. Constraints on the coupling parameters simplify the field equations considerably. We arrive at a quasi-Einstein equation and a wave equation for the aether field. Finally, we discuss a simple solution of this model found by Baekler
