Once, there was a Golden Age, where beings with powers beyond imagining walked the Earth. Now, however, all of the gods, really strong mages, Precursors and whatnot are gone, or shadows of what they once were. Fortunately, this means the great demons and monsters are also weaker than they once were, but unfortunately, modern society is far less capable of dealing with them.
This is actually a very old myth indeed: in Antiquity the belief was that man had declined from a Golden Age. The Greek poet Hesiod theorized that 'the present' (ie. the mundane world) is only the latest and most bleak period of human history. It was not until much later that the view that human history is one of relentless progress truly caught on. The Roman poet Ovid copied this progression, with the Golden Age followed by Silver, Bronze, and Iron Ages in his epic Metamorphoses, all declining in quality. Hesiod had a 'Heroic' Age, populated by demigods and heroes, in between the Bronze and Iron (present) Ages.
Hindu philosophers invented a similar concept, of the four yugas, which delineated a series of stages in the moral evolution and subsequent devolution of the universe, at large. The main events of both the major Epics fall at the end of an Era, leaving the world to the 'lesser sons of greater sires'. This use of devolution is very popular across the Fantasy genre, and any series set in The Time of Myths usually implies by the end that magic and the Gods will either retire or die off, leading to a society similar to the viewer's, though this might have less to do with cynicism, and more to do with emulating J.R.R. Tolkien.
It can be argued that this Twilight gives a type of freedom from the tyranny of the gods, or from the temptation the magical/technological power that destroyed The Ancients. Also, whereas former evils back then could only be sealed, now the overall entropy means they can die.
The remnants of the past are a common plot device. Discovering the ruins of an Advanced Ancient Acropolis is a common quest. Pockets of the Lost Technology that the old ones understood and wielded freely become treasures, either as one-of-a-kind Black Box constructs or as the foundation of the technology level of the new world. A survivor might even exist in the form of a Living Relic. Of course, the fearful may (rightly) stigmatize and seek to destroy these relics for fear they are Pointless Doomsday Devices.
Usually, when the old civilization was human, it is explicitly based on the Roman Empire, especially its fall and the state of Europe afterwards. Occasionally, the people visiting are aliens, robots, or stranger fare paying respects to Humanity's Wake.
Sometimes, there is a promise of a bright future ahead, as good as or better than the old world. If so, it's usually either caused directly or helped along by the efforts of the protagonists. Still even in this last case the series will have an unavoidable sense of wistfulness. Magic is, well magical after all, and it is hard not to mourn its loss.
See Also: And Man Grew Proud, After the End, Here There Were Dragons, The Magic Goes Away, Precursors and End of an Age. Not to be confused with the expletive that demands that the Big Man Upstairs condemns something that just screwed you over.
For more information on this trope, consult The Encyclopedia of Fantasy's entry on "Thinning".