In most cases once can safely use the default values for ENCUT and ENAUG, which are read from the POTCAR file. But there are some cases where this can results in small, easily avoidable inaccuracies.
For instance, if you are interested in the energy difference between bulk phases with different compositions (i.e. Co - CoSi - Si). In this case the default ENCUT will be different for the calculations of pure Co and pure Si, but it is preferable to use the same cutoff for all calculations. In this case determine the maximal ENCUT and ENAUG from the POTCAR files and use this value for all calculations.
Another example is the calculation of adsorption energies of molecules on surfaces. To minimize (for instance) non-transferable wrap errors one should calculate the energy of an isolated molecule, of the surface only, and of the adsorbate/surface complex in the same supercell, using the same cutoff. This usually requires to fix ENCUT and ENAUG by hand in the INCAR file. If one also wants to use real space optimization (LREAL=On), it is recommended to use LREAL=On for all three calculations as well (the ROPT flag should also be similar for all calculations, section 6.39).