The collected current by spherical and cylindrical Langmuir probes immersed in an unmagnetized and collisionless non-Maxwellian plasma at rest are theoretically studied, and analytical expressions for the currents of attracted and repelled plasma particles are presented. We consider Kappa, Cairns and the generalized Kappa–Cairns distributions as possible models for the velocity field in the plasma. The current–voltage characteristics curves are displayed and discussed. Furthermore, comparisons with the collected currents in Maxwellian plasmas are given. The results of Particle-in-Cell (PIC) simulations of spherical and cylindrical probes in non-Maxwellian plasmas are also presented, and compared with the theoretical expressions. The results for the collected currents by the Langmuir probes obtained by PIC simulations are in good agreement with the corresponding analytical expressions.