Nearly every JLI character was either killed, turned evil, or otherwise made tragic during Dan DiDio's administration of DC Comics. This earned him a lot of fan hate.
The final Super Buddies series even made a Take That! to Identity Crisis by having a running gag in which Sue Dibny was believed to be pregnant. (She was killed in IC while apparently being pregnant) Although it wasn't an intentional Take That!. I Can't Believe It's Not the Justice League had been complete for a while but for whatever reason (most likely due to Ralph and Sue's roles in Identity Crisis) held off on publishing it before finally releasing it as an arc in the JLA Classified series. Originally the pregnancy jokes were just a Running Gag but after Identity Crisis became Harsher in Hindsight.
Ensemble Darkhorse: Blue Beetle, Booster Gold, Guy Gardner, Fire, and, to a lesser degree, Ice all gained a fair deal of popularity thanks to their appearances in this series. DC would eventually capitalise on the popularity of Booster and Guy, with Booster getting a large role in 52 and an ongoing series and Guy going to Green Lantern Corps, making them Breakout Characters.
Harsher in Hindsight: In their very first scene, the natives of the Kooey Kooey Kooey island are complaining that offering it for a new JL embassy was a massively bad idea. Fast forward to the grand finale of Giffen's run, where Dreamslayer kills them all.
From the same story: Booster jokingly tells the Beetle that he cannot wait to get back to New York so Max Lord can put a bullet between his eyes. Cue to Countdown to Infinite Crisis, where Max Lord shoots the Blue Beetle in the head.
The series' frequent use of self-deprecating humor had a somewhat negative impact on the cast after the book was cancelled, with most of the characters branded as incompetent jokesters by their fellow superheroes. Blue Beetle was probably hit the hardest by this, being regarded as an annoying buffoon right up until his violent death.
The Super Buddies mini-series essentially opened with a Where Are They Now segment showing just how far most of the JLI members had fallen since their time on the League. For instance, Fire was reduced to operating a soft-core porn website, and L-Ron was now shown working at a burger joint.
Though things did eventually get better for some of the members. Fire went on to join Checkmate after Super Buddies, the team was eventually reformed during Brightest Day.
Subverted with Guy Gardner. He went from a forgettable extra Green Lantern to one of the more popular characters in the series thanks to his role in JLI.
Also subverted with Booster Gold as he was already viewed as a bit of an incompetent glory hound before the series (and loved by readers for that very reason). As the exposure the series lead to Booster appearing in more series, his writers capitalized on the JLI's infamy by having Booster use his reputation to his advantage.
Tear Jerker: The funeral issue for Mr. Miracle was this from beginning to end.