We study the star formation rate (SFR) - stellar mass (M*) relation in a self-consistent manner from 0 < z < 2.5 with a sample of galaxies selected from the NEWFIRM Medium-Band Survey. We find a significant non-linear slope of the relation, SFR propto M*^0.6, and a constant observed scatter of 0.34 dex, independent of redshift and M*. However, if we select only blue galaxies we find a linear relation SFR propto M*, similar to previous results at z = 0 by Peng et al. (2010). This selection excludes red, dusty, star-forming galaxies with higher masses, which brings down the slope. By selecting on L_IR/L_UV (a proxy for dust obscuration) and the rest-frame U-V colors, we show that star-forming galaxies fall in three distinct regions of the log(SFR)-log(M*) plane: 1) actively star-forming galaxies with normal dust obscuration and associated colors (54% for log(M*) > 10 at 1 < z < 1.5), 2) red star-forming galaxies with low levels of dust obscuration and low specific SFRs (11%), and 3) dusty, blue star-forming galaxies with high specific SFRs (7%). The remaining 28% comprises quiescent galaxies. Galaxies on the normal star formation sequence show strong trends of increasing dust attenuation with stellar mass and a decreasing specific SFR, with an observed scatter of 0.25 dex (0.17 dex intrinsic scatter). The dusty, blue galaxies reside in the upper envelope of the star formation sequence with remarkably similar spectral shapes at all masses, suggesting that the same physical process is dominating the stellar light. The red, low-dust star-forming galaxies may be in the process of shutting off and migrating to the quiescent population.
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