We computationally explore how the orientation of dipolar emitters placed near plasmonic nanostructures affects their radiative enhancement and spontaneous emission rate. We demonstrate that the expressions for these quantities show a subtle dependence on the molecular orientation, and this information is lost when typical calculations assume a random orientation and perform an average over all directions. This orientation dependence is strongly affected by the location of the emitter, the emission wavelength, and the symmetry of the system. While the plasmonic nanostructure can significantly modify the far-field from a molecule in its vicinity, this modification is heavily dependent on both the wavelength and the orientation of the emitter. We show that if a fluorescent molecule can be constrained to emit in a specific direction, we are able to obtain far superior control over its spontaneous emission and decay rate than otherwise and discuss implications for single molecule experiments.