It's fashionable these days in some quarters both Christian and Buddhist to say that hell (and heaven) are just states of mind here in the human realm. This is clearly not what the Buddha taught about other realms. In the Sangarava Sutta (Majjhima 100), for instance, he was asked straight out whether or not there really are gods. His answer was definitive;
As for hell, there is quite a long depiction of the torments in Niraya (hell) found in the Devaduta Sutta, Majjhima 130, complete with many gruesome details. It comes as a shock to many westerners interested in Buddhism that we do have our own fire-and-brimstone literature.
When this was said, the brahmin student Sangarava said to the Blessed One: "Master Gotama's striving was unfaltering, Master Gotama's striving was that of a true man, as it should be for an Accomplished One, a Fully Enlightened One. But how is Master Gotama, are there gods? (devas)"
"It is known by me to be the case, Bharadvaja, that there are gods."
Of course, there are crucial differences between the Christian conception of hell and the Buddhist. Most importantly, the Buddhist hell, and the Buddhist heaven too, are not eternal. They are considered as stations of rebirth. As well, hell was not created by anyone as a place of punishment. It is a natural result of certain karmas, particularly the karma of violence and cruelty.
The rationalists are already objecting; but this isn't a real place. By raising this objection they are revealing their adherence to the naive assumption that this human realm is a real place. So is hell real? What do you mean by "real", grasshopper?
The universe we actually live in, the only one we can ever know directly, is the product of our own mind. True, we get faulty and limited signals from some mysterious "out there" in the form of light waves striking the eyes, pressure on the nerve endings, sound-waves striking the ear. But the world we actually experience is fabricated from this external data mediated through the physical apparatus of our senses and the mental apparatus of perception.
There have been schools of Buddhism that postulated that there is no real external universe. This has not been the position of the Theravada. We admit the reality of an external world, we're just not all that interested in it. Why bother about something we can only know second or third hand?
So, we could say that we dream this human world, but the dreaming is constrained by various inputs of data from an external world. The other realms are also experienced as dreams, perhaps somewhat less constrained by the incoming data. The Zen master Dogen once wrote something about how a man, a demon, a naga and a ghost all experience the same river differently. This is much stronger than the modern psychological interpretation, it does posit quite different states of being. However, there is also no reason to rule out the traditional Theravadin interpretation that heaven and hell are actual "places" existing as whole realms distinct from this plane of reality. In fact, it seems quite naive to assume that this realm is the only one.
The existence of heaven and hell make perfect sense within the system of karma and rebirth. A being is reborn according to their predominant karmas and cravings. If these are of an extreme nature, either towards goodness or evil, then the karmic-resultant will also be extreme and for instance, one who has lived by killing and torturing will be reborn into a sphere of killing and torturing.
However, it must not be forgotten that the point of Buddhism in the end is to escape from all of these insubstantial, impermanent and imperfect realms and end the cycle of karma and rebirth once and for all.
Here are a few links for those who haven't raised enough hell yet
The Afterlife in Different Religions
Comparison of Christian and (Mahayana) Buddhist beliefs
Catholic Encyclopedia article on Hell
Tibetan Buddhism article on Hell (scroll down past the Google ads)
Dante's Inferno Test. Which circle of hell is right for you?
And of course, this venerable chestnut; Is Hell exothermic or endothermic?