Check that the light's Illuminates by Default attribute is on when no light linking is intended.
Make sure Cast Shadows or Receive Shadows are turned on for the object.
If a shadow depth map is expected, check that Enable Depth Maps is turned on in Render Settings window (Windows > Rendering Editors > Render Settings).
If a raytraced shadow is expected, check that the Ray Depth Limit (for the light and in Render Settings window) are turned up to a sufficient limit.