We present the stellar mass functions (SMF) and mass densities of galaxies, and their spheroid and disk components in the local (z∼0.1) universe over the range 8.9 ≤ log(M/M ⊙ ) ≤ 12 from spheroid+disk decompositions and corresponding stellar masses of a sample of over 600,000 galaxies in the SDSS-DR7 spectroscopic sample. The galaxy SMF is well represented by a single Schechter function (M * = 11.116 ± 0.011, α = −1.145±0.008), though with a hint of a steeper faint end slope. The corresponding stellar mass densities are (2.670±0.110), (1.687±0.063) and (0.910±0.029)×10for galaxies, spheroids and disks respectively. We identify a crossover stellar mass of log(M/M ⊙ ) = 10.3±0.030 at which the spheroid and disk SMFs are equal. Relative contributions of four distinct spheroid/disk dominated sub-populations to the overall galaxy SMF are also presented. The mean disk-to-spheroid stellar mass ratio shows a five fold disk dominance at the low mass end, decreasing monotonically with a corresponding increase in the spheroidal fraction till the two are equal at a galaxy stellar mass, log(M/M ⊙ )=10.479±0.013; the dominance of spheroids then grows with increasing stellar mass. The relative numbers of composite disk and spheroid dominated galaxies show peaks in their distributions, perhaps indicative of a preferred galaxy mass. Our characterization of the low redshift galaxy population provides stringent constraints for numerical simulations to reproduce.