We present results from an adaptive optics survey for substellar and stellar companions to Sun-like stars. The survey targeted 266 F5-K5 stars in the 3Myr to 3Gyr age range with distances of 10-190pc. Results from the survey include the discovery of two brown dwarf companions (HD49197B and HD203030B), 24 new stellar binaries, and a triple system. We infer that the frequency of 0.012-0.072Msun brown dwarfs in 28-1590AU orbits around young solar analogs is 3.2% (+3.1%,-2.7%; 2sigma limits). The result demonstrates that the deficiency of substellar companions at wide orbital separations from Sun-like stars is less pronounced than in the radial velocity brown dwarf desert. We infer that the mass distribution of companions in 28-1590AU orbits around solar-mass stars follows a continuous dN/dM_2 ~ M_2^(-0.4) relation over the 0.01-1.0Msun secondary mass range. While this functional form is similar to that for <0.1Msun isolated objects, over the entire 0.01-1.0Msun range the mass functions of companions and of isolated objects differ significantly. Based on this conclusion and on similar results from other direct imaging and radial velocity companion surveys in the literature, we argue that the companion mass function follows the same universal form over the entire range between 0-1590AU in orbital semi-major axis and 0.01-20Msun in companion mass. In this context, the relative dearth of substellar versus stellar secondaries at all orbital separations arises naturally from the inferred form of the companion mass function.