Since the "mantle" of Green Lantern is actually a position in an intergalactic police force, it makes sense that there are so many active claimants to the title. With five human Green Lanterns currently operating (only the four Flashes come close to matching this), Blackest Night has the difficult job of giving all of them something to do. Fortunately, the preceding arcs in Green Lantern and Green Lantern Corps (not to mention some peeks ahead at DC's solicitations for the next few months) provide a good sense of what we can expect for each Green Lantern.
To be honest, it can all be summarized fairly simply - figure out which dead characters meant the most to each Lantern (particularly if they were named by Death in Green Lantern #43), and assume they'll be meeting those particular Black Lanterns very soon.
Hal Jordan will, of course, be the star of the show. The most recent Green Lantern arcs found Hal struggling with his own despair and hopelessness, and one can only hope he can find something worth fighting for (not to mention worth truly living for) in the pages of Blackest Night. Beyond his own emotional arc, there's his relationship with Carol Ferris, who is now a member of the newly formed Star Sapphire Corps. I'm guessing the two of them are going to find some time to talk things out, although it'll probably be in the midst of some massive interstellar battle.
There are a lot of potential Black Lanterns that would likely hit him close to home - his Justice League teammates Aquaman and Martian Manhunter are obvious examples - but I think two potential candidates really stand out in my mind as having particular meaning to Hal Jordan. More obviously, there's Abin Sur, his predecessor as Green Lantern, whose death is integral to Hal's origin story. Even more emotionally crushing would be his father Martin Jordan, a test pilot whose plane exploded in front of young Hal's eyes. Geoff Johns's run on Green Lantern, from Green Lantern: Rebirth to the "Secret Origins" arc, has taken great pains to define Hal as a person whose fearlessness and brashness are in reaction to the terror of witnessing the death of his father. I'm guessing Blackest Night will feature the payoff to all that setup.
John Stewart has one really obvious deceased character in his past - his wife, the Green Lantern Katma Tui. Their reunion is pretty much a certainty, considering the Star Sapphire Yrra Cynril (formerly his nemesis Fatality) has already foretold their meeting. (It's also mentioned in one of DC's upcoming solicitations). Speaking of Yrra Cynril, there's also her entire planet of Xanshi, which John Stewart infamously allowed to be destroyed in the Cosmic Odyssey story back in the eighties. He's more at peace with his mistake than he has been in the past, but it's possible Blackest Night may give him an opportunity for some real closure, even if it involves an entire planet of Black Lanterns.
Kyle Rayner has dealt with a whole lot of death in his time, particularly during his tenure as the last Green Lantern in existence. He still grieves over the death of his mother, whose memory helped him through his imprisonment within the Parallax entity during Sinestro Corps War. His girlfriend Alexandra DeWitt was notoriously killed off and stuffed in a refrigerator, which became emblematic of the often shoddy treatment of female characters in comic books in general. (There's also his girlfriend Jade, but I think she's better dealt with when we get to another Green Lantern on this list.) In the here and now, there's his current lover Soranik Natu, the Green Lantern of Korugar and quite probably the long lost daughter of Sinestro. I'm guessing their fates will be intertwined as Blackest Night plays out.
Guy Gardner is probably the least touched by death of all the Green Lanterns. Admittedly, quite a few of his comrades from his time in Justice League International are not only dead but also mentioned in Green Lantern #43, including Ted Kord, Ralph and Sue Dibny, and Maxwell Lord. Even so, Guy has come a long way from his days as a violent idiot in the Keith Giffen Justice League (well, he's still kind of violent and idiotic, but he's more respected now), and I'm not entirely sure those characters would have even close to the same emotional impact of some of the others I've mentioned.
Instead, I suspect Guy Gardner's central interest in Blackest Night will be protecting his beloved Ice, who was recently resurrected and was named by Death as one of the heroes it wants back. For all their recent failures to make their relationship work, Guy Gardner cares about Ice probably more than just about anyone in the DC universe, and I'd be shocked if he doesn't do everything in his power to protect her.
Then there's Alan Scott, the Golden Age Green Lantern who isn't even part of the Corps at all. His roles in both Green Lantern: Rebirth and Sinestro Corps War weren't much more than glorified cameos, but there are a couple of reasons to think he will have more to do in Blackest Night. For one thing, the second batch of tie-in miniseries will include Blackest Night: JSA, and with all due respect to the rest of the Justice Society, you would have to think Alan Scott will take center stage there. Besides, while he didn't necessarily have the clearest stakes in the previous two stories, Alan Scott is arguably the Green Lantern most affected by the prospect of dead characters returning from the grave.
As a Golden Age character who was active in World War II, his chronological age is probably somewhere in the early nineties, even if various plot contortions have kept him considerably younger. As such, most of his would-be contemporaries are dead simply because of the march of time, meaning there are considerably more potential Black Lanterns in his past than the younger Green Lanterns. But above all, there's his daughter, Jenny-Lynn Hayden, better known as Jade. During the recent "Thy Kingdom Come" arc in Justice Society of America (written, incidentally, by Geoff Johns), Alan Scott openly wondered whether the godlike being Gog could bring his daughter back to life. Of all the Black Lanterns I hope ultimately receive a proper resurrection, I'm probably hoping for Jade more than anyone else.