It is extremely difficult to generalize at what pressures or temperatures the deviation from the ideal gas becomes important. As a rule of thumb, the ideal gas law is reasonably accurate up to a pressure of about 2 atm, and even higher for small non-associating molecules.  For example, methyl chloride, a highly polar molecule and therefore with significant intermolecular forces, the experimental value for the compressibility factor is  at a pressure of 10 atm and temperature of 100 °C.  For air (small non-polar molecules) at approximately the same conditions, the compressibility factor is only  (see table below for 10 bars, 400 K).