When people who are unfamiliar with effect sizes learn that various effect size indexes such as R2 are generated automatically by SPSS or STATA, the temptation is to report their R2 and just leave it at that.
But the coefficient of multiple determination, or R2, may not be a particularly useful index as it combines the effects of several predictors. If you are interested in the effect of a specific predictor, rather than the omnibus effect arising from all the variables in your model, you might want to consider other options such as the relevant beta coefficient (standardized or unstandardized, depending on what you plan to do with it).
Another option is to report the relevant semipartial or part correlation coefficient which represents the change in Y when X1 is changed by one unit while controlling for all the other predictors (X2, … Xk). Although both the part and partial correlations can be calculated using SPSS and other statistical programs, the former is typically used when “apportioning variance” among a set of independent variables (Hair et al. 1998: 190).
For a good introduction on how to interpret coefficients in non-linear regression models, see Shaver (2007).