This is an issue guide for the current JLA comic book, first published in 1996 by DC Comics. "JLA" has received acclaim, partly because it features (nearly) all the Big Wheels of the DC Universe, partly for writer Grant Morrison's killer dialogue, partly for his world-shaking storylines. It's good stuff. Most of the issues listed below -- particularly all of Morrison's and most of Mark Waid's and Joe Kelly's -- are highly recommended.
This guide also contains special issues, like the "Midsummer's Nightmare" mini-series, the Secret Files issues, and all the annuals I could find.
BE WARNED: all of these contain LOTS of spoilers -- if you don't want to know what happened, don't click on the issues below...
Justice League: A Midsummer's Nightmare #1 (by Mark Waid, Fabian Nicieza, Jeff Johnson, and Darick Robertson)
Justice League: A Midsummer's Nightmare #2 (by Mark Waid, Fabian Nicieza, Jeff Johnson, and Darick Robertson)
Justice League: A Midsummer's Nightmare #3 (by Mark Waid, Fabian Nicieza, Jeff Johnson, and Darick Robertson)
JLA Secret Files and Origins #1 - vs. mind-controlling starfish (by Grant Morrison, Mark Millar, and Howard Porter)
JLA #1 - vs. the Hyperclan (by Grant Morrison and Howard Porter)
JLA #2 - vs. the Hyperclan, part 2 (by Grant Morrison and Howard Porter)
JLA #3 - vs. the Hyperclan, part 3 (by Grant Morrison and Howard Porter)
JLA #4 - vs. the Hyperclan, part 4 (by Grant Morrison and Howard Porter)
JLA #5 - introducing Tomorrow Woman (by Grant Morrison and Howard Porter)
JLA #6 - vs. Heaven and Hell (by Grant Morrison and Howard Porter)
JLA #7 - vs. Heaven and Hell, part 2 (by Grant Morrison and Howard Porter)
JLA #8 - vs. the Key (by Grant Morrison and Oscar Jimenez)
JLA #9 - vs. the Key, part 2 (by Grant Morrison and Oscar Jimenez)
JLA #10 - Rock of Ages, part 1 (by Grant Morrison and Howard Porter)
JLA #11 - Rock of Ages, part 2 (by Grant Morrison and Howard Porter)
JLA #12 - Rock of Ages, part 3 (by Grant Morrison and Howard Porter)
JLA #13 - Rock of Ages, part 4 (by Grant Morrison and Howard Porter)
JLA #14 - Rock of Ages, part 5 (by Grant Morrison and Howard Porter)
JLA #15 - Rock of Ages, part 6 (by Grant Morrison, Howard Porter, Gary Frank, and Greg Land)
JLA Secret Files and Origins #2 - reforming the JLA (by Christopher Priest and Yanick Paquette)
JLA #16 - vs. Prometheus (by Grant Morrison and Howard Porter)
JLA #17 - vs. Prometheus, part 2 (by Grant Morrison and Arnie Jorgensen)
JLA #18 - vs. weird-ass coincidences (by Mark Waid and Howard Porter)
JLA #19 - vs. weird-ass coincidences, part 2 (by Mark Waid and Howard Porter)
JLA #20 - prisoners of Adam Strange (by Mark Waid and Arnie Jorgensen)
JLA #21 - prisoners of Adam Strange, part 2 (by Mark Waid and Arnie Jorgensen)
JLA #22 - vs. giant dream-controlling starfish (by Grant Morrison and Howard Porter)
JLA #23 - vs. giant dream-controlling starfish, part 2 (by Grant Morrison and Howard Porter)
JLA #1,000,000 - vs. the future JLA (by Grant Morrison and Howard Porter)
JLA #24 - vs. the Ultramarine Corps (by Grant Morrison and Howard Porter)
JLA #25 - vs. the Ultramarine Corps, part 2 (by Grant Morrison and Howard Porter)
JLA #26 - vs. the Ultramarine Corps and the General (by Grant Morrison and Mark Pajarillo)
JLA #27 - vs. Amazo (by Mark Millar and Mark Pajarillo)
JLA #28 - JLA/JSA Team-Up (by Grant Morrison and Howard Porter
JLA #29 - JLA/JSA Team-Up, part 2 (by Grant Morrison and Howard Porter)
JLA #30 - JLA/JSA Team-Up, part 3 (by Grant Morrison and Howard Porter)
JLA #31 - JLA/JSA Team-Up, part 4 (by Grant Morrison and Howard Porter)
JLA #32 - trying to clean up Gotham City (by Mark Waid, Devin Grayson, and Mark Pajarillo)
JLA #33 - vs. Bruce Wayne (by Mark Waid and Mark Pajarillo)
JLA #34 - the world's worst prison riot (by Grant Morrison and Howard Porter)
JLA #35 - vs. the Spectre (by J. M. DeMatteis and Mark Pajarillo)
JLA #36 - World War III, part 1 (by Grant Morrison and Howard Porter)
JLA #37 - World War III, part 2 (by Grant Morrison and Howard Porter)
JLA #38 - World War III, part 3 (by Grant Morrison and Howard Porter)
JLA #39 - World War III, part 4 (by Grant Morrison and Howard Porter)
JLA #40 - World War III, part 5 (by Grant Morrison and Howard Porter)
JLA #41 - World War III, part 6 (by Grant Morrison and Howard Porter)
JLA #42 - vs. germs (by Dan Curtis Johnson and Mark Pajarillo)
JLA #43 - vs. Ra's Al Ghul (by Mark Waid and Howard Porter)
JLA #44 - vs. Ra's Al Ghul, part 2 (by Mark Waid and Howard Porter
JLA #45 - vs. Ra's Al Ghul, part 3 (by Mark Waid and Howard Porter)
JLA #46 - vs. Ra's Al Ghul, part 4 (by Mark Waid and Steve Scott)
JLA #47 - vs. The Queen of Fables (by Mark Waid and Bryan Hitch)
JLA #48 - vs. The Queen of Fables, part 2 (by Mark Waid and Bryan Hitch)
JLA #49 - vs. The Queen of Fables, part 3 (by Mark Waid, Bryan Hitch, and Javier Saltares)
JLA #50 - vs. Dr. Destiny (by Mark Waid, Bryan Hitch, Phil Jimenez, Ty Templeton, Doug Mahnke, and Mark Pajarillo)
JLA #51 - superheroes vs. secret identities (by Mark Waid and Mike S. Miller)
JLA #52 - superheroes vs. secret identities, part 2 (by Mark Waid and Bryan Hitch)
JLA #53 - superheroes vs. secret identities, part 3 (by Mark Waid and Bryan Hitch)
JLA #54 - superheroes vs. secret identities, part 4 (by Mark Waid and Bryan Hitch)
JLA: Our Worlds at War - vs. Imperiex (by Jeph Loeb and Ron Garney)
JLA #55 - Return of the White Martians (by Mark Waid and Bryan Hitch)
JLA #56 - More of the Return of the White Martians (by Mark Waid and Mike S. Miller)
JLA #57 - Revenge of More of the Return of the White Martians (by Mark Waid and Mike S. Miller)
JLA #58 - Attack of the Revenge of More of the Return of the White Martians (by Mark Waid and Mike Miller)
JLA #59 - vs. Jokerized Dr. Polaris (by Chuck Dixon, Scott Beatty, and Darryl Banks)
JLA #60 - How the JLA Saved Christmas! (by Mark Waid and Cliff Rathburn)
JLA #61 - vs. tidal waves, giant monsters, and suchlike (by Joe Kelly and Doug Mahnke)
JLA #62 - The Golden Perfect, Part I (by Joe Kelly and Doug Mahnke)
JLA #63 - The Golden Perfect, Part II (by Joe Kelly and Doug Mahnke)
JLA #64 - The Golden Perfect, Part III (by Joe Kelly and Doug Mahnke)
JLA #65 - The Greatest Danger of All: Parenthood (by Joe Kelly and Doug Mahnke)
JLA #66 - The Destroyers, Part I (by Joe Kelly and Doug Mahnke)
JLA #67 - The Destroyers, Part II (by Joe Kelly and Doug Mahnke)
JLA #68 - Mysteries of Atlantis (by Joe Kelly and Doug Mahnke)
JLA #69 - All New! All Different! (by Joe Kelly and Yvel Guichet)
JLA #70 - Stranded in ancient Atlantis (by Joe Kelly and Doug Mahnke)
JLA #71 - Replacement JLA vs. drought (by Joe Kelly and Yvel Guichet)
JLA #72 - Grim revelations in ancient Atlantis (by Joe Kelly and Doug Mahnke)
JLA #73 - Replacement JLA vs. Giant Zombie Bitch (by Joe Kelly and Yvel Guichet)
JLA #74 - In this issue...EVERYBODY DIES! (by Joe Kelly and Doug Mahnke)
JLA #75 - Everyone vs. Gamemnae (by Joe Kelly, Doug Mahnke, Yvel Guichet, Darryl Banks, and Dietrich Smith)
JLA #76 - Aftermath of all that Atlantis stuff (by Joe Kelly, Lewis La Rosa, and Al Milgrom)
JLA #77 - vs. Mnemon (by Rick Veitch and Darryl Banks)
JLA #78 - Rules of Engagement, Part 1 (by Joe Kelly and Doug Mahnke)
JLA #79 - Rules of Engagement, Part 2 (by Joe Kelly and Doug Mahnke)
JLA #80 - The White Rage, Part 1 (by Joe Kelly and Duncan Rouleau)
JLA #81 - The White Rage, Part 2 (by Joe Kelly and Duncan Rouleau)
JLA #82 - The White Rage, Part 3 (by Joe Kelly and Duncan Rouleau)
JLA #83 - The War in Ira--uhh, Qurac (by Joe Kelly and Chris Cross)
JLA #84 - Trial by Fire, Part 1 (by Joe Kelly and Doug Mahnke)
JLA #85 - Trial by Fire, Part 2 (by Joe Kelly and Doug Mahnke)
JLA #86 - Trial by Fire, Part 3 (by Joe Kelly and Doug Mahnke)
JLA #87 - Trial by Fire, Part 4 (by Joe Kelly and Doug Mahnke)
JLA #88 - Trial by Fire, Part 5 (by Joe Kelly and Doug Mahnke)
JLA #89 - Trial by Fire, Part 6 (by Joe Kelly and Doug Mahnke)
JLA #90 - Bats and Wondy sittin' in a tree... (by Joe Kelly and Chris Cross)
JLA #91 - vs. a Space Monkey (by Dennis O'Neil and Tan Eng Huat)
JLA #92 - vs. a Space Monkey, Part II (by Dennis O'Neil and Tan Eng Huat)
JLA #93 - vs. a Space Monkey, Part III (by Dennis O'Neil and Tan Eng Huat)
JLA #94 - The Tenth Circle, Part I (by Chris Claremont, John Byrne, and Jerry Ordway)
JLA #95 - The Tenth Circle, Part II (by Chris Claremont, John Byrne, and Jerry Ordway)
JLA #96 - The Tenth Circle, Part III (by Chris Claremont, John Byrne, and Jerry Ordway)
JLA #97 - The Tenth Circle, Part IV (by Chris Claremont, John Byrne, and Jerry Ordway)
JLA #98 - The Tenth Circle, Part V (by Chris Claremont, John Byrne, and Jerry Ordway)
JLA #99 - The Tenth Circle, Part VI (by Chris Claremont, John Byrne, and Jerry Ordway)
JLA #100 - vs. the Elite (by Joe Kelly and Doug Mahnke)
Special Issues
JLA: Earth 2 - vs. the mirror universe JLA (by Grant Morrison and Frank Quitely)
JLA/WildC.A.T.s - DC and Image superteams vs. the Lord of Time (by Grant Morrison and Val Semeiks)
JLA: Welcome to the Working Week - Stowaway in the Watchtower (by Patton Oswalt and Patrick Gleason)