Trouble From the Past

It's The Future (or Alternate Universe), whether bright and shiny or gritty and violent, and as if its residents didn't have enough on their minds, an major issue from their civilization's collective Dark and Troubled Past arises once more and has to be dealt with ASAP, kicking off the plot. Said issue may have something to do with Great Offscreen Wars, Forgotten Superweapons, deadly diseases still on the loose, but not necessarily. Often, the nature of the issue is the object of the author's criticism of contemporary state of the world (so expect the future generations to go "What an Idiot!!" over their ancestors' actions); this trope lends itself well to Green Aesops.

A Super-Trope to both Sealed Evil in a Can (where the past generations' mistake was to seal the evil, rather than destroy it) and Sins of Our Fathers (where the "generation" part requires literal direct descent). Break Out the Museum Piece may be required to deal with it.

Anime and Manga

 * The interdimensional community in the Lyrical Nanoha series is more or less a technological Utopia still reeling from the Belkan War 80 years ago. Every season so far has revolved around a piece of Belkan legacy from said war.
 * The whole purpose of in Ergo Proxy is to clean up Earth's ruined environment for humanity

Literature

 * The Beautiful Faraway series by Sergey Lukyanenko is set on a future Earth where humanity mastered everything there was to master, but heavily damaged its own genetic code in the process. Because of this, one of the protagonists cannot have children with the woman he loves, as their genes would produce dangerous mutations if combined.
 * It would seem all past to us, but in the Deryni works, the twelfth century Gwynedd has to deal with the evils done in the ninth and tenth centuries (invasion and conquest, a nasty Magocracy, a rebellion that leads to a backlash, and then two more centuries of Fantastic Racism).
 * In Uglies by Scott Westerfeld, people in the future still have to clean up the hole in the ozone layer and contain a species of nigh-invulnerable genetically engineered ecosystem-destroying orchids.

Live-Action TV

 * In the Star Trek Verse we have the Eugenics Wars of the mid-1990s, the "sanctuary districts" of the early 21st century where the homeless, jobless, and mentally ill were left to rot, and the post-atomic horror following World War Three in the late 21st century.
 * In Star Trek IV: The Voyage Home, the humans of the past hunted whales to extinction... and that turned out to be a bad idea.
 * In WALL-E, the people who return to Earth still have to clean up their ancestors' mess of garbage.

Video Games

 * Final Fantasy X works on this principle. The inhabitants of Spira all consider Sin to be their punishment for not following Yevon's teachings. A summoner must in order to vanquish Sin for 10 years. Then, it comes back again. The player attempts to find a way around this clause.
 * Half of the problems in the entire Fallout series are leftovers from the past, either in the form of radiation, old world machines, or other leftover messes.

Western Animation

 * The future of Futurama may not be a utopia, but poverty has been mostly eliminated; however, it came at the expense of many a Dystopian Edict. The unemployed are forced to take jobs against their will, the remaining poor have been sent to insane asylums, and mutants are forced to live in the sewers. Also, in the episode "A Big Piece of Garbage", the people of the 31st century have to deal with the garbage problems of the 21st century.