"We of the endless are the servants of the living--we are not their masters. WE exist because they know, deep down in their hearts, that we exist. When the last living thing has left this universe, then our task will be done. And we do not manipulate them, if anything, they manipulate us..."
Dream, from Brief Lives

They are not gods and anyone who tells you otherwise is either misinformed or looking for a rhyme that goes with purple. They are The Endless. They are personifications of concepts which have existed since before mankind dreamed of gods and will continue to exist long after the last god is dead. They are not royalty or nobility exactly but are usually treated as such, as each has jurisdiction and responsibilities over their respective namesakes. They are not our gods and we are not theirs, but they are more like servants to us than we are of them. They are more powerful than most entities in reality, but this does not place them any particular place on any chain of command or pecking order for immortal beings. In fact, they're not even immortal. They just live longer than most anything -- even longer than most immortals.

They are embodiments of their namesakes: Destiny is the oldest brother and spends too much time with his nose in a book. Death is the oldest sister and it is believed she will outlive everyone else. Dream was born soon after, and was the first to die only to be replaced. Destruction tried to enjoy his job but after awhile went into early retirement. Desire is actually twins in the same body which rather defeats the whole purpose of having twins. Despair does not wear clothes very often, is into pain, and should get out more. Delirium used to be Delight but something happened and now she's just watching birds paddle with wrenches better than the chicken before the egg. Oh, and she's the youngest.

jujuben23 pointed out to me: "there is a slight error. Dream was not, in fact, the first to die and be replaced, Despair was. It's not something that's talked about much, but in the last omnibus volume, it discusses this, iirc, when the new Dream is talking to the one responsible for Morpheus's death." I concur, but there's a reason they don't talk about it much. Dreams do die. Most humans (and assumedly inhumans) don't like to think that destinies can die. =)

Neil Gaiman wrote a comic book series about them which examined culture and history, pointing out where and when The Endless have affected humanity. Of course it's all fiction, and if you believe that, I have a word that rhymes with purple which I'd be happy to sell to you.