When I was a kid, I absolutely loved issues about new members joining, and I committed to memory the issue numbers where the JLA ranks changed. The JLA was the cream of the crop of the DCU; being asked to join--or in the rare case of when someone left--was a big deal, and in the original JLA comic it was treated as a cause for celebration. I think the whole JLA concept lost something intangible yet vital when members started coming and going with barely a mention.
The story: "Doom of the Star Diamond" by Gardner Fox, Mike Sekowsky, and Bernard Sachs. An alien (another alien!) named Carthan has been exiled off his planet by an evil despot; so he goes to the JLA for help(I guess Oa was too far away?). But for complicated reasons he can't contact them directly, so he kidnaps Green Arrow, who just happened to be accepted as the JLA's newest member! What luck he didn't kidnap, say, Sargon the Sorcerer, otherwise no one would've cared.
After a whole bunch of hugger-mugger(note:"hugger-mugger" is equal to much hurried activity in Earth terms!), all the JLA get trapped in giant diamond, and only Green Arrow with his deus ex machina arrow can free them.
Roll Call: Superman, Batman, Wonder Woman, Aquaman, Flash, Green Lantern, Martian Manhunter, and new member Green Arrow
Notable Moments: Green Arrow joins! Yay! During the meeting, Flash suggests Adam Strange, and Batman suggests Hawkman. I think it would've been a hilarious running gag if, every time they had a new member meeting, Flash kept offering up Adam Strange and no one ever listened to him.
Mike Sekowsky, often derided at the time finally got his artistic due years later. As a kid, his jerky body poses, which upset a lot of fans, didn't bother me at all, and they still don't. Plus, he had such an awesome facility for laying out a page that despite all that Fox crammed in in any given panel, the storytelling is clear and concise.
Young letter writer Roy Thomas writes in to suggest Green Arrow for membership. Hey, that kid could have a career writing comics!
On a separate note, while reading this comic once, I was met with the Nightmare of the Sticky Tape--the piece of tape holding the plastic bag closed got stuck to the cover. Try as I might I couldn't get it free without it taking off a huge chunk of Aquaman's(Aquaman! oh, the irony!) face. But apparently that didn't stop me from trying to make a bad situation worse. A little marker, and...
...oh yeah, that's much better.
One last thing--Julius Schwartz admitted many years later that the only reason Green Arrow--who had his own feature at the time of the JLA's creation--wasn't included was because he plum forgot about him!
He later said that Aquaman was thrown in mostly because he had his own strip, too, and possibly if he had remembered Arrow, Aquaman might've been dropped since he thought that, at the time, "seven characters were enough."
Well, speaking as an Aquaman fan, I can only thank Mr.Schwartz for his faulty memory, because Aquaman being one of the original seven gained him a place in comic book--and possibly even pop-culture--history, and to know he was that close from not making it in...*shudder*
But hey, at least Green Arrow didn't have to wait long!

He later said that Aquaman was thrown in mostly because he had his own strip, too, and possibly if he had remembered Arrow, Aquaman might've been dropped since he thought that, at the time, "seven characters were enough."
Well, speaking as an Aquaman fan, I can only thank Mr.Schwartz for his faulty memory, because Aquaman being one of the original seven gained him a place in comic book--and possibly even pop-culture--history, and to know he was that close from not making it in...*shudder*
But hey, at least Green Arrow didn't have to wait long!