We map out the first excited state sublevel structure of single nitrogen-vacancy (NV) colour centres in diamond. The excited state is an orbital doublet where one branch supports an efficient cycling transition, while the other can simultaneously support fully allowed optical Raman spin-flip transitions. This is crucial for the success of many recently proposed quantum information applications of the NV defects. We further find that an external electric field can be used to completely control the optical properties of a single centre. Finally, a group theoretical model is developed that explains the observations and provides good physical understanding of the excited state structure.