Superman: Grounded went through this largely due to writer J. Michael Stracynski leaving the book about halfway in. Chris Roberson took over in the second half, and largely retooled the arc to abandon Stracynski's original premise.
Peter J. Tomasi's run was cut short when Brian Michael Bendis signed onto DC and was given the Superman titles. Some things were dropped because of this.
The entire series hinted that Jonathan Kent and his neighbour Kathy Branden were going to get together, with her being present for his significant moments and the two fighting off Manchester Black together. She disappears when Bendis started writing, and because he aged up Jon in order to make him the Superboy of the Legion of Super-Heroes, Jon would instead form a relationship with Saturn Girl (who happens to have the same telepathic powers as Kathy).
When Jonathan Kent, Kathy Branden and Damian Wayne are involved in a fight with Manchester Black that results in time energy escaping and giving them visions, we see a vision of a square Earth and Damian Wayne as Batman, Jonathan Kent as Superman and an adult Kathy. The run had previously already featured a future where Damian and Jon apparently died, after Damian did something to Jon that Future Tim Drake considered monstrous, with Future Damian being revealed to have survived Future Tim's attempt on his life. This is never explained and Jon, under Bendis, does not interact with Damian nearly as much as he did under Tomasi.
Tony Bedard: I was going to have Blaze create a trio of henchgirls called the Furies. Remember Siobhan's roommate and her two friends? They were all orphaned in superhero battles and had sworn themselves to finding a way to make super-people pay. They were going to beat Supergirl and take her back to Blaze's home dimension. Hilarity would ensue. I wanted to get Siobhan in there more, to make her and Kara a team. I had one issue where the newly Red Lanterned Kara fights Silver Banshee, and I contrasted their fight with flashbacks of Kara and Siobhan just having fun roommate moments. That remains one of my favorite things from the run: just letting her have a friend. Michael returns in my final issue, and we’ll see if they do anything with him after that. If not, it was enough that Kara met a guy who had every reason to hate life and yet retained a positive outlook. He was in many ways a good role model for her, and he didn’t want to trick or use her, which is nice for a change. And Shay I wanted to keep playing sort of mysterious. Is she really a friend to Supergirl, or does she view her as another science project? Shay’s still a bit of a cypher to me, which is okay if she’s played for mystery. But I liked doing scenes of her staff at the Block talking about what it’s like being stuck there, having to wear her face, alternating between admiration and resentment. It gave the whole Block set-up a little complexity.
In Bizarrogirl, Superwoman's cell gets damaged when Bizarrogirl's ship crash-lands, implying she might get loose in the future. Sterling Gates confirmed she was supposed to get free and join a "Supergirl Revenge Squad" kind of villain team, but that subplot was dropped when he left the book and forgotten when Flashpoint rebooted the universe.
Supergirl (2005): Good Looking Corpse: The end of Nick Spencer's first issue showed a montage of teen superheroes being targeted by the arc’s villain, including Static, Blue Beetle, Miss Martian, Damian Wayne, Batgirl (Stephanie Brown) and Impulse (Irey West). The subsequent issues were supposed to see Supergirl team up with those characters as part of a Backdoor Pilot for a new Young Justice series with the same cast, but this was all dropped once Spencer was prematurely removed from the book. While Damian and Blue Beetle did still guest star in subsequent issues, that was pretty much the only remnant of the original Young Justice revival plan.
"The Super-Steed of Steel": Supergirl is wondering aloud if there may be some way to grant Comet's dream to become human, her super-horse says there IS a way, but he cannot tell her yet. However, Comet found another method to become -temporarily- human in planet Zerox, and it was never revealed what he meant by "The time is not ripe".
Supergirl (Rebirth): The DC Year of the Villain/Event Leviathan tie-in was completely hijacked by the Infected arc after its first issue and wasn't returned to before the series ended. The plot threads that Kara's adoptive father Jeremiah was fighting against Leviathan and that his wife Eliza possibly joined them against him were left unresolved.
In related series R.E.B.E.L.S., featuring Vril Dox II, an ancestor of Brainiac 5's from the 20th century, the earlier Dox makes a deal with Neron in exchange for knowledge, offering up not his own somewhat tarnished soul, but instead placing the debt on his bloodline and setting it to come due in "about 1000 years." After R.E.B.E.L.S. was canceled, a team of Legionnaires was sent back to the 20th century, leading to a meeting between Querl and his ancestor in which Vril mentioned Neron in a guilty sort of way...and then nothing came of it. It was implied, however, that the insanity of Brainiac 5's mother could be related to this deal.
Prior to this, a number of long-running subplots started during the TMK run were dropped unceremoniously because of the Zero Hour reboot. Some of these were quickly condensed into a panel or two in the final issue, but others were just forgotten. Most notably, Sussa Paka (formerly the villain Spider Girl) steals a mysterious sealed canister from the corrupt Earthgov branch of the Science Police (secretly under the control of the alien Dominators). On the run from the cops, she gets caught up in the Legion's battle to liberate Earth. Eventually, she shows up on the Legion's doorstep looking for protection, and immediately gets caught up in their problems. She grows fond of the team, and ultimately joins up, adopts a new name (Wave) and a new hair color...but events start cascading from there, and the actual contents of the canister that half the galaxy was ready to kill Sussa to get their hands on are never revealed.
Many arcs were dropped when Geoff Johns stopped writing the Legion back-up feature in Adventure Comics, which included Lightning Lad investigating the possibility that his older brother might've actually had a twin, the Legion of Super-Villains having their own espionage squad in the 21st Century, Dream Girl being held hostage, and the connection Kid Flash and XS had to Professor Zoom's ongoing war with the Flash Family. The story about Dream Girl was retconned, and the Lightning Lad subplot was briefly carried over into the new ongoing Legion comic where Garth had to drop his search because Saturn Girl and their kids disappeared during the destruction of Titan.
Live-Action TV
Lois & Clark: The New Adventures of Superman: Towards the end of an arc, the Corrupt Corporate Executive was defeated and killed, and his (apparently) dumb-blonde trophy wife Mindy was last seen saying that she would be in charge from now on, with an implication that perhaps she had been the prime mover all along. She made one subsequent appearance (again successfully framing someone else for her crimes), and was never mentioned again.
Western Animation
Legion of Super-Heroes: Both Drax and Alexis are forgotten about after their debut episodes, though the latter makes a brief cameo on Takron Galtos in "Sundown".
The two-parter "Little Girl Lost: Part 1" and "Little Girl Lost: Part 2" ended with Clark planning to introduce Jimmy to Kara, hinting at the start of a possible romance as Jimmy had been at Supergirl's side when she investigated Intergang. However, Jimmy ended up crushing on another girl in his next major role and he and Supergirl never interacted again.
:Tony Bedard: I was going to have Blaze create a trio of henchgirls called the Furies. Remember Siobhan's roommate and her two friends? They were all orphaned in superhero battles and had sworn themselves to finding a way to make super-people pay. They were going to beat Supergirl and take her back to Blaze's home dimension. Hilarity would ensue. I wanted to get Siobhan in there more, to make her and Kara a team. I had one issue where the newly Red Lanterned Kara fights Silver Banshee, and I contrasted their fight with flashbacks of Kara and Siobhan just having fun roommate moments. That remains one of my favorite things from the run: just letting her have a friend. Michael returns in my final issue, and we’ll see if they do anything with him after that. If not, it was enough that Kara met a guy who had every reason to hate life and yet retained a positive outlook. He was in many ways a good role model for her, and he didn’t want to trick or use her, which is nice for a change. And Shay I wanted to keep playing sort of mysterious. Is she really a friend to Supergirl, or does she view her as another science project? Shay’s still a bit of a cypher to me, which is okay if she’s played for mystery. But I liked doing scenes of her staff at the Block talking about what it’s like being stuck there, having to wear her face, alternating between admiration and resentment. It gave the whole Block set-up a little complexity.