2000s: DC: The New Frontier
DC: The New Frontier #1-6, by Darwyn Cooke
Kyle Rayner would enjoy some success as the main (and, in fact, only) Green Lantern for a number of years before Hal Jordan would return as the “main” Green Lantern. Fortunately, the Green Lantern Corps concept allows for other Lanterns such as John Stewart, Guy Gardner, and Kyle Rayner to all exist alongside one another.
That said, the best Green Lantern book of the decade is still New Frontier. The book is a beautifully illustrated rumination on the shift from the Golden Age of Comics to the Silver Age as a reflection on changes in American history and politics in the real life years between the late 1950s and early 1960s. But even with all that, the backbone of the book is a Hal Jordan story, as what hero could better represent Kennedy's America than a playboy with ambitions of landing on the moon?
And, look, I hear you grumbling. Yes: Rebirth and Sinestro Corps War and Blackest Night were all exciting stories that exploited Green Lantern continuity to its fullest and brought a ton of new readers to the title, but if you think there's even a single panel in any of those stories that is better or more affecting than the scene in which Hal tries to remember how to say “the war is over” in Korean, I am officially calling you a liar.
Best of the rest: “Sinestro Corps War” (Green Lantern: Sinestro Corps Special #1, Green Lantern vol 4 #21-25, Green Lantern Corps vol 2 #14-19), “Secret Origin” (Green Lantern vol 4 #29-35), Willworld, Green Lantern Corps: Recharge #1-5, Green Lantern: Rebirth #1-6
And that's it for the decades we've experienced so far! The 2010s are halfway over; we'll have to see who comes out on top in five years! Will anything beat Red Lanterns: Blood Brothers? We'll see!