No one has been able to definitively answer this question. While there are some hints that ghosts might exist in Hill House, it is also likely that the characters (especially the neurotic Eleanor) are experiencing psychological disturbances. However, these two interpretations are not mutually exclusive.
The Haunting of Hill House is a classic example of Gothic literature. One of the principal themes of Gothic literature is how the evils of the past linger in the present and continue to oppress the living. Hill House is a haunted house, so it fits that mold.
The house was built by a rather disturbed man, Hugh Crain. The interiors are stuffy and "Victorian." Crain stressed fire-and-brimstone theology to keep his two daughters in line. When he died, his daughters fought over who got to keep the house. So it seems the house was endowed with a malignant energy from the very beginning.
Indeed, the house itself seems to be evil, bringing out the worst in whoever is inhabiting it and consuming them in the end (which happens to Eleanor who becomes so attached to the house that she is ultimately unable to ever leave it). This interpretation combines both the material and supernatural views of the nature of Hill House-- the supernatural brings out the worst in the people living there, and then they set about causing their own ill fortunes.
Of course, that is just one way of looking at it. As mentioned previously, no one knows for sure and that is what has helped keep the book a classic.