The ideal gas law applies to real gases only when the real gas is under certain conditions:

1. The gas must be under fairly low pressure, so that the molecules
   1. are very far apart compared to their actual volume and
   2. do not interact except through collisions.
2. The gas must be within a limited volume so that there is no appreciable gravitational force gradient within the volume of the gas.

When a real gas is under high pressure or is near its boiling point, so that the gas molecules are almost in contact, it no longer behaves ideally because molecular volume and intermolecular interactions become significant.

Under common conditions, real gases mimic an ideal gas so well that we can determine absolute zero (the temperature at which an ideal gas goes to zero volume) pretty accurately from their temperature-volume behavior.

For an example of factors for which non-ideal behavior of real gases is important, see this answer.