Hal Jordan met a rogue Lantern named Malvolio, who used a Batman Gambit to get Hal to replace his own ring with Malvolio's and leave. What this was supposed to accomplish was never followed up on, though many fans pointed to it later as a way to press the Reset Button on Hal's badly done Face–Heel Turn. (In the end, the Button was pressed a different way.)
Another example is Gerard Jones' characterization of the Guardians of the Universe. Throughout his 45 issues on the book, Jones planted many clues that related to his plans for the Guardians. When Executive Meddling changed the plans, many of the odd behaviors of the Guardians (and characters' observations of same) were left dangling and unresolved.
Character profiles of the various Lantern Corps introduced characters who seemed like they would be plot-relevant, particularly the "Lost Sapphire" who was clearly intended to be important. This teasing never went anywhere.
A number of these have come out such as the other six new laws in the Book of Oa and the Lost Star Sapphire. Made even weirder by the fact that the writer who set most of them up, Geoff Johns, was on the book for another several years afterward, and never explored any of them.
Hal Jordan and the Green Lantern Corps eventually brings in Kyle Rayner in his White Lantern form, before he loses those powers and becomes a Green Lantern once again. Kyle's last appearance prior to this series was in The Omega Men, which involved him joining a terrorist organisation called the Omega Men, and after becoming disillusioned with the notion of superheroics and growing to sympathise with the Omega Men's fight against the evil organisation the Citadel, helped the Omega Men overthrow said Citadel, wearing a new costume and being dubbed the Omega Lantern. He returns to Earth at the end of the story and is asked where his loyalties lie, and it's implied that they lie with the Omega Men. Nothing in The Omega Men is touched on in Hal Jordan and the Green Lantern Corps.
The Emerald Warriors series had several arcs. The mapping of the Unknown Sectors, Sodom Yat organising a Daxamite rebellion against the Guardians, an ancient telepath manipulating the selection process for Green Lanterns, and then running off with Sodom himself... all completely ignored after War of the Green Lanterns. Jeez.
The Krona and Relic arc from Lost Army seems to have been forgotten, Not to mention an answer to who sent the Green Lanterns to the previous universe in the first place. At least the whereabout of the Templar Guardians was finally addressed.
Lord Malvolio of the Green Flame, a half-human Green Lantern, dressed like Alan Scott, who was hundreds of years old and who manipulated Hal into taking his ring. Malvolio planned to use Hal in his war against the Old Timer, but this plot thread remains unresolved.
Evil Star was implied to be behind Black Hand's death touch upgrade, was definitely behind the Shark's upgrade, and was stated to have destroyed a Blue Lantern's homeworld. When he turned up in Grant Morrison's Green Lantern run, none of this was addressed.
Both of the arcs in Green Lanterns revolving around the Phantom Ring end in ways suggesting a potential follow-up that was ultimately never made, with "The Phantom Lantern" ending with Frank Laminski vowing to reclaim the Phantom Ring and get his revenge as he's carried away to one of the Watchtower's holding cells and the series' final arc "Evil's Might" ending with Cyborg Superman escaping with the Phantom Ring while promising to get even with the Green Lantern Corps for thwarting his efforts to destroy the rebuilt Coast City.
Geoffrey Thorne's Green Lantern run ended with John Stewart taking on the new costumed identity of the Emerald Knight, with the final page teasing a series utilizing this new direction for the character. However, due to a change in plans for John behind the scenes, the ensuing John Stewart: The Emerald Knight project was downgraded to a one-shot special, and the character subsequently returned to his original Green Lantern identity in time for the Green Lantern: War Journal series.
