I've been known to make the most of my sizable RPG collection, and this is definitely in that vein. The players take on the roles of characters from the same family, or from historically intertwined families, at a certain point in history. Every few sessions, the GameMaster makes time move forward to another time period, where the players play only slightly different characters, the descendants of their former characters!
GURPS might make an excellent system for this kind of campaign because of all its historical world books. So you might start in the Ice Age (one of my favorites), move on to Atlantis and its destruction, then to Greece, Imperial Rome, Middle Ages, Scarlet Pimpernel, Old West, World War II, something modern like Cops or Special Ops, and beyond to Cyberpunk, Terradyne and Traveler!
An enterprising GameMaster would surely be able to do the same with a completely fantastical setting, perhaps as simply as making various D&D settings be different epochs. What if the World of Greyhawk is merely the Forgotten Realms in the far past? Much better would be advancing the politics/society and magic/technology ahead by a few generations so that the world is still recognizable, but totally different in each era. Think of how Star Trek morphed into The Next Generation.
Back and Forth
The beauty of this concept is that there is no reason you couldn't go back to a past era for a session with the ol' gang even if you're past it in the "Saga". Maybe you just miss your ancient Egyptians, maybe you make it part of the action as a "reveal" of a character's heritage (for example, a character might tell a story passed down from generation to generation).
What You Leave Behind
There are three ways to link the various eras you use. One is to make the transition an important event in the era you're leaving. The Atlantis era, for example, might end with the characters narrowly escaping the island's sinking and landing in Greece, setting up the next chapter. Their descendants' capture by Roman hands, might set up the Spartacus chapter to come, and so on.
Then there's the family heirloom. A sword/amulet/secret/curse passed down through the generations would identify a character and its progeny and keep a sense of telling the same story. Some objects might not last the thousands of years necessary, unless you make them magical (Excalibur has been pulled out of a stone in many SF stories).
And the third is the characters themselves. While each era would feature different characters, they'd be close enough to the originals that 1) you wouldn't be trapped in chargen hell every few weeks and 2) you could keep the sense of family alive. The sins of the father are visited on the child. Characters are doomed to repeat the same mistakes, get into the same kind of trouble, pile on the historical ironies. Subplots aren't abandoned when you make the switch, they are just ported to the next era in some familiar form. Character A and his descendants are all unlucky in love, character B and hers both lost a child, etc.
So What's the Story?
Each era has its own type of adventure. You can just go along with it. The premise is that the families of these characters have a long tradition of being adventurers (likely unbeknownst to them, even). Or if an "heirloom" is important enough, then it is the saga of that MacGuffin and how it survived through the ages, always surrounded by men and women of determination or action. Sky's the limit and history is a looooong time...