We present results on the charge dependence of the radiative recombination lifetime, Tau, and the emission energy of excitons confined to single self-assembled InGaAs quantum dots. There are significant dot-to-dot fluctuations in the lifetimes for a particular emission energy. To reach general conclusions, we present the statistical behavior by analyzing data recorded on a large number of individual quantum dots. Exciton charge is controlled with extremely high fidelity through an n-type field effect structure, providing access to the neutral exciton (X0), the biexciton (2X0) and the positively (X1+) and negatively (X1-) charged excitons. We find significant differences in the recombination lifetime of each exciton such that, on average, Tau(X1-) / Tau(X0) = 1.25, Tau(X1+) / Tau(X0) = 1.58 and Tau(2X0) / Tau(X0) = 0.65. We attribute the change in lifetime to significant changes in the single particle hole wave function on charging the dot, an effect more pronounced on charging X0 with a single hole than with a single electron. We verify this interpretation by recasting the experimental data on exciton energies in terms of Coulomb energies. We show directly that the electron-hole Coulomb energy is charge dependent, reducing in value by 5-10% in the presence of an additional electron, and that the electron-electron and hole-hole Coulomb energies are almost equal.