Nearly every JLI character was either killed, turned evil, or otherwise made tragic during Dan DiDio's administration of DC Comics. This earned them 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.)
It wasn't an intentional Take That mind you. 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.
Ho Yay: Between Beetle and Booster, gradually increasing as the series went on. By the time of Super Buddies, even the writers were openly acknowledging it in the stories.
Never Live It Down: 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.
Tearjerker: The funeral issue for Mr. Miracle was this from beginning to end.