Give fresh information about the characters. Discard an epilogue that regurgitates the final chapter and does not add anything new. Unless when writing genre fiction, abandon an epilogue that adds a "twist" and sows doubt about the denouement. Twists in the epilogue will only irritate the reader by stealing the satisfaction of a full resolution.
Describe what happens in a different time and a different place. According to Nancy Kress, author of the novel "Probability Sun," epilogues should take place far away from the time and location of the denouement of the story. For example, in an epic spanning several generations, it may serve to describe the fate of grandchildren. In an epic featuring inter-galactic voyages, you can use the epilogue to draw attention to what happens in planet left far behind.
Resist the temptation to start a new thread of the story. The story was over in the final chapter. Starting another story in the epilogue will rob the reader of satisfaction derived from the story's resolution.
Use epilogues to drop hints of a sequel. This works best in detective stories and murder mysteries. Hollywood thrillers often employ epilogues that can go something like this: the murderer is executed, and the town is safe from the serial killer. But the next morning, the charming waitress is discovered dead. The camera zooms into the sheriff's drawer. You see a knife. It's bloody. Could it be him?
Keep it short. An epilogue should be "proportional" to the work, says Kress. Use a long epilogue if your story has hundreds of characters and runs into a thousand pages. An epilogue to "War and Peace," for example, is longer than one to a relatively short novel like "On the Road." As a general rule, keep the epilogue as short as you can.