Plot Archaeology

A plot arc that was incomplete and forgotten, and then suddenly brought back out of the blue to continue the plot arc itself. This is distinct from the Continuity Cavalcade and Continuity Porn tropes in that it's not just a Shout-Out type situation - the plot arc is resumed, essentially where it left off.

In short, what distinguishes Plot Archaeology from similar tropes is that it's not just a one-episode reappearance as a Shout-Out.

Examples of Plot Archaeology include:

Anime and Manga

In Durarara!!, the slasher is mentioned early on a couple times but not addressed until much later.

Comic Books

X-Men: Mystique reveals her true form to Nightcrawler, who is shocked that they look very similar. She mentions his mother's name. 10 YEARS (or more) later, it's revealed that she is his mother. It hadn't been even mentioned in the comics in-between those two points.
- The Third Summers Brother. In 1993, Mr Sinister casually refer to Cyclops having "brothers", then corrects himself. This arc got aborted when Fabian Nicieza left the X-titles before he could reveal the third brother was Adam-X, the X-Treme. Over the next ten years, the concept was never referred to. (Robert Weinberg thought it was Apocalypse, but also left the book before he could say so). In 2004 Chris Claremont suddenly brought it up again, and revealed it was Gambit, but that was in an Alternate Continuity. Then, in 2006, Scott and Alex finally meet Gabriel Summers, aka Vulcan. Unfortunately, Vulcan's backstory makes it impossible that Sinister could have known about him in order to make that casual offhand reference. Fans now wonder if there's a fourth Summers brother.

Literature

In the Anita Blake series, the events of book 11 resulted in the vampire serial killing group Anita was after not actually getting caught. Fans bitched and complained when the next few books didn't mention it at all, and then in Book 17 LKH went back to it and we finally get to confront the Big Bad. A few other loose threads from that were also left hanging in that book and the one right after it are still waiting to be picked back up though.

Live-Action TV

In the first season of Heroes, Hiro falls in love with a waitress named Charlie. It turns out she has a brain tumor and is going to die. Hiro accepts that he can't save her, gets some Character Development, and the plot moves on. Several seasons later, Hiro regrets that he didn't save her, and the arc focuses on her again as Hiro goes back in time to try and save her, but she gets kidnapped and held hostage by the Big Bad.
News Radio had a storyline where Lisa decided she wanted to have a baby with Dave. This went on for a few episodes, then was quietly dropped. In a later episode the same season, there is a brief conversation about how the moment had passed. The writers hated continuing story lines, which the network continually tried to force on the show.
The First Evil from Buffy the Vampire Slayer makes a one-off appearance in season 3. It shows up four seasons later as the Big Bad.
Stargate Atlantis: Stardrives were mentioned very briefly in an early episode and didn't become massively important until the finale three seasons later.
Doctor Who introduced River Song in "Silence of the Library" but was otherwise quickly dropped, then brought back with the Eleventh Doctor.
- It's a habit. Arc Words sometimes get planted before they're even used in a this-is-leading-up-to-something fashion. We get a briefly-seen newspaper mention of "Saxon" being ahead in the polls midway through new series season two. Nothing is said of it until "Mister Saxon" becomes a mystery figure of season three.
In Star Trek: The Next Generation, Wesley Crusher is built up as being a very special person, and it is suggested that he would do something remarkable, eventually. Then he was phased out of the show, and was gone for something like three seasons. Come the final season, the Creator's Pet returns, and the plot arc completes itself.
At one point, Ugly Betty had a plot arc about Amanda trying to discover the identity of her biological father. After a few episode, the plot disappeared with no resolution. In the show's Grand Finale, Amanda finds her father, out of the blue and completely by accident.
In Sliders, the Kromaggs were a season two Monster of the Week who got one mention in season three. Then comes a Channel Hop... and their return as the franchise Big Bad.
On The Wire, McNulty's FBI buddy gives him the results of an unfinished investigation that showed Lt. Daniels was dirty when he was on the Narcotics task force. McNulty doesn't trust him for most of the first season, but eventually the men grow to respect each other. This is not mentioned again until the series finale, when now-Commissioner Daniels is forced to resign rather than be manipulated by the threat of revealing that very same investigation.

Western Animation

Avatar: The Last Airbender, one episode introduces Bato from Katara and Sokka's father Hakoda's fleet, and suggests the kids can meet up with the fleet. When this fails, no further attempts are made to meet up with Hakoda or the fleet until the third season.
At one point in Superman: The Animated Series, Brainiac blasts former partner Lex Luthor with a ray that (like many instances of Where Did They Get Lasers) doesn't seem to hurt him much for what appeared to be intended as a killshot. Much much much later in Justice League Unlimited, we find that that's because it actually wasn't. Brainy put his data inside Lex in case he was destroyed, and this backup of himself was now needed. Enter... Brainithor! The Powers That Be have said that they'd actually planned it the day they wrote the zapping scene, they just didn't the right opportunity to use it for a long, long time.
In Transformers Animated, Porter C. Powell makes a single not-terribly-memorable appearance in the first season and it doesn't look like he's intended to return. In season two, he does... with a vengeance.