The concept of the formation of a solute-sized cavity in a solvent is widely used in the theories of solvation processes; however, most of the studies of cavity formation using atomistic simulations were limited to water and hydrocarbon models. We calculated the Gibbs free energy of cavity formation ΔcavG for a structurally diverse set of 23 common organic solvents. For the calculation, molecular dynamics simulations of solvent boxes were conducted, and the Widom particle insertion method was applied. The results obtained with two different force fields for the same solvent were in good agreement with each other in most cases. The obtained cavity size dependences of ΔcavG allowed ranking the solvents by the free energy cost of creation of a cavity with a certain size. Surprisingly, this cost was somewhat higher in glycerol, formamide, and ethylene glycol than in water. In general, higher values of ΔcavG are observed for the solvents with a branched network of intermolecular hydrogen bonds and strongly polar aprotic solvents. The numerical results can be used to improve the accuracy of the calculation of the cavity term in non-aqueous continuum solvation models.