We report on measurements of single-molecule Brownian motion in liquid crystals, unravelling the anisotropic mobility of individual dye molecules. This anisotropic Brownian motion is directly correlated with the structural properties in a smectic A (8CB) and a nematic (5CB) liquid crystal sample cell on the micrometer scale using polarization contrast microscopy. A considerably slower mobility of dye molecules is found as compared to self-diffusion measurements by NMR, while anisotropy values compare well to recent literature data. This is suggested to be related to local distortions of the director structure around the dye molecules.