The project Massive Unseen Companions to Hot Faint Underluminous Stars from SDSS (MUCHFUSS) aims at finding hot subdwarf stars with massive compact companions like massive white dwarfs (M>1.0M_{sun}_), neutron stars, or stellar-mass black holes. The existence of such systems is predicted by binary evolution theory, and recent discoveries indicate that they exist in our Galaxy. We present orbital and atmospheric parameters and put constraints on the nature of the companions of 12 close hot subdwarf B star (sdB) binaries found in the course of the MUCHFUSS project. The systems show periods between 0.14 and 7.4days. In nine cases the nature of the companions cannot be constrained unambiguously whereas three systems most likely have white dwarf companions. We find that the companion to SDSSJ083006.17+475150.3 is likely to be a rare example of a low-mass helium-core white dwarf. SDSSJ095101.28+034757.0 shows an excess in the infrared that probably originates from a third companion in a wide orbit, which makes this system the second candidate hierarchical triple system containing an sdB star. SDSSJ113241.58-063652.8 is the first helium deficient sdO star with a confirmed close companion. This study brings to 142 the number of sdB binaries with orbital periods of less than 30 days and with measured mass functions. We present an analysis of the minimum companion mass distribution and show that it is bimodal. One peak around 0.1M_{sun}_ corresponds to the low-mass main sequence (dM) and substellar companions. The other peak around 0.4M_{sun}_ corresponds to the white dwarf companions. The derived masses for the white dwarf companions are significantly lower than the average mass for single carbon-oxygen white dwarfs. In a T_eff_-logg diagram of sdB+dM companions, we find signs that the sdB components are more massive than the rest of the sample. The full sample was compared to the known population of extremely low-mass white dwarf binaries as well as short-period white dwarfs with main sequence companions. Both samples show a significantly different companion mass distribution indicating either different selection effects or different evolutionary paths. We identified 16 systems where the dM companion will fill its Roche Lobe within a Hubble time and will evolve into a cataclysmic variable; two of them will have a brown dwarf as donor star. Twelve systems with confirmed white dwarf companions will merge within a Hubble time, two of them having a mass ratio to evolve into a stable AMCVn-type binary and another two which are potential supernova Ia progenitor systems. The remaining eight systems will most likely merge and form RCrB stars or massive C/O white dwarfs depending on the structure of the white dwarf companion.