One of my all-time favorite issues of the JLA!
The story: "The Case of the Disabled Justice League!" by Gardner Fox, Mike Sekowsky, and Bernard Sachs. Some of the JLAers stage a mock battle with a giant alien to entertain some handicapped children.
While battling, they find themselves handicapped--Superman goes blind, Hawkman develops asthma, etc. They learn to overcome their handicaps to face several other attacks. Turns out its all a plot of the evil Brainstorm, who ends up controlling them with his mind powers. The other Leaguers show up and help defeat them and then Brainstorm.
Roll Call: Superman, Batman, Wonder Woman, Aquaman, Flash, Green Lantern, Martian Manhunter, Green Arrow, Atom, Hawkman
Notable Moments: This issue ends, of course, with the handicapped kids learning that since the JLA overcame their handicaps, they can too! Flash then tells them that this case was very similar to an adventure the JSA had(in All-Star Comics #27), and they make the same pledge the JSAers did:
...sure, this story is about as subtle as getting whacked by a two by four, but its heart is so firmly in the right place that it doesn't matter.
This story was reprinted in the classic Super Friends treasury comic, and that's where I first read it--a perfect story to represent the inherent goodness and decency of the Justice League of America.