3. The Legion of Super Pets
Krypto the Super-Dog. Streaky the Super-Cat. Comet the Super-Horse. Beppo the Super-Monkey. The Pooch of Power. The Feline of Force. The Mare of Might. The Simian of Steel. Imbued with Kryptonian powers, these super-pets were gathered together by the Legion of Superheroes to defeat mind-controlling aliens, owing to the fact that the aliens could not control the minds of animals. To my mind, more than anything, this suggests that these animals, despite being physically capable of enormous destruction, simply do not have the mental heft required for higher thinking of any kind, be it tactical, moral, or otherwise, and should be regarded less as superheroes than as a force of nature to be feared, barely restrained by some kind of dimly understood obligation to their super-masters. To collect all these animals in one place and expect them to be able to complete any kind of mission rather than tear each other and the surrounding area to absolute shreds is a ludicrous bet at best and an act of mass manslaughter at worst.
And god help us all if they ever get super-rabies.
2. The Great Lakes Avengers
Less effective than even the West Coast Avengers, whose members collaboratively conceived and birthed children that turned out to be fragments of the devil's soul, the Great Lakes Avengers represent the best the American midwest has to offer. Actually, the Great Lakes Avengers aren't actually called that anymore, because they got a cease and desist from the real Avengers, telling them they couldn't use that name. So they went ahead and renamed themselves the Great Lakes X-Men. They've gone through a few other ill-advised name changes (the Great Lakes Defenders, for one, and the Thunderbolts rip-off, Lightning Rod), finally settling on the Great Lakes Initiative, but the problems with these folks run a lot deeper than branding. The more notable members include leader Mr. Immortal, who revives when he dies, but is pretty much a normal, vulnerable guy up until that point; Big Bertha, who can control her body fat; Doorman, who can teleport anything into the next room; Grasshopper, who died after accidentally jumping into space; and the infamous Squirrel Girl, who can talk to squirrels, and does so). By contrast, the only hero the GLA have ever rejected was Leather Boy, a BDSM fetishist who misunderstood what kind of "costumed adventurers" they were looking for (he later killed Squirrel Girl's pet squirrel for revenge). Their status as a haven for misfits did inspire this ripping rock ballad, though, and after all, everyone's gotta fit in somewhere.
1. The Justice Society of America
Oh, boy, the Justice Society of America.
The JSA are the Indian burial ground that the whole DC Comics universe is built atop, simultaneously its foundation and the source of its woes. Predating the Justice League by a decade, 1940's All Star Comics #3 includes the first ever superhero team, featuring the original bowl-helmet Flash and the weak-against-wood Green Lantern, the first appearance of Wonder Woman (as their goddamn secretary), and Superman and Batman as founders and honorary members. The series saw the team battling super crime and fighting in World War II (though they were unable to invade Europe, because Hitler had a magic spear, obviously). With declining sales, though, the title ended, and the characters stayed dormant until their revival at the start of the Silver Age and the creation of the Justice League, featuring a new Flash and Green Lantern, but the same Batman, Superman, and Wonder Woman. That's where the trouble started.
As it turns out, DC decided that the JSA and the JLA actually occupied alternate universes, thereby sidestepping the dicey chronology. These were helpfully called "Earth-One" and "Earth-Two," as revealed in the landmark crossover between the two teams, "Crisis on Earth-One." Having blown the door open on alternate universes, DC used that explanation gleefully and indiscriminately, creating new universes to fix continuity glitches, house characters and teams acquired from other companies, and as a hail mary plot point.
1985's Crisis on Infinite Earths was DC's attempt to deal with the universal bloat that the JSA set off. However, by merging the Golden and Silver Age universes, DC sentenced itself to decades of bending over backwards to keep the continuity even moderately sensible (e.g., If the JSA fought in World War II, why aren't they older?) (You guessed it: magic!). DC managed to write them out in the late 80's, trapping them in a recreation of Ragnarok, but because there was money to be made, they brought them back.
The JSA opened the door for older superheroes (without which we wouldn't have the incredibly bad-ass Clint Eastwood-esque Bruce Wayne from Batman Beyond), mind-bending alternate universe tales, and the very idea of the superhero team-up, but their creation opened Pandora's box, letting out egregious retconning, resurrections, convoluted continuity, multiverse bullshit, and ruining characters for profit. Everything that's horrible in comics, the JSA are responsible for.
So: The Justice Society of America!
Honorable Mention: The Super Globetrotters
The Harlem Globetrotters are superheroes. Didn't you know? (Disqualified for never appearing in a comic book, re-qualified for one of the members being a horrifying human basketball, and re-disqualified for the same reason.)