The members of Flash's rogues gallery frequently team up. Does that count?

captain cold and heat wave used to team up, I think.

There is the Earth-Two Wonder Woman's Villainy Inc ensemble, in which Diana's rogues gallery escaped from the Amazon Reformation Island and caused mayhem. However, supervillain teamups are rare in themselves, apart from ensemble groups like Villainy Inc, the Earth-One Flash's Rogues Gallery, Earth-Two's Injustice Society, Earth-One's Injustice Gang, the Legion of Super-Villains (although Lightning Lord, Saturn Queen and Cosmic King could be worth bearing in mind there) and the Fatal Five. On the whole, supervillains seem to be more individualistic than their heroic counterparts*, with the above exceptions and those John has already noted. And of course, there are also Earth-Three's Crime Syndicate, Earth-S' Monster Society of Evil and other isolated exceptions.

*Probably because they want sole control over the proceeds of crime.

Over time, apart from Batman and the Flash, the number of ensemble supervillains has been trimmed down somewhat, and some DC superheroes have no regular, recurrent adversaries altogether. Others have one or so apiece- Atom and Chronos, Aquaman and Ocean Master or Black Manta, Green Arrow and Merlyn, Green Lantern and Sinestro, Superman, Luthor and Brainiac, Wonder Woman and the Cheetah. Black Canary, Hawkman and Hawkwoman, the Martian Manhunter, Red Tornado and Zatanna had conspicuously few recurring adversarial characters. On Earth-One, only Batman and the Flash have sizeable collaborative rogues galleries. On Earth-Two, the Injustice Society seems to have vacuumed up all of the enduring and more persistent supervillains, with exceptions like the Psycho Pirate. Given Earth-Three's inverted morality, it's the Crime Syndicate. Earth-Four's Sentinels of Justice don't seem to have accumulated elaborate rogues galleries of their own, and it's fair to say that the relative weakness of its original universe may have contributed to the eclipse of Charlton in the late sixties. Earth-S had the advantage of revival of the Fawcett ensemble during the seventies and a new lease of life for Captain Marvel's rogues gallery as a consequence. Even there, Sivana and Mr Mind seem to work alone, apart from the Monster Society of Evil and Thad's family. Earth-X is a special case, given that the Nazis probably liquidated all the uncooperative Freedom Fighters adversaries or conversely, co-opted the more opportunist or rabid fascist fellow travelers. Earths C and C Minus appear to have revived funny animal supervillains, new characters or funny animal parodies of Earth-One villains against the Zoo Crew and Justa Lotta Animals. As for Hoppy the Marvel Bunny, no-one comes to mind except Captain Black Bunny, who appears to be a rabbit version of Black Adam.

Doc, I take your point about the Sportsmaster and Huntress, but they're a special case insofar as Earth-Two goes. Apart from the Harlequin and Green Lantern, and Hawkman and Hawkgirl, and later Fury and the Silver Scarab, I can't think of many heroic or villainous collaborations on Earth-Two outside the Injustice Society and Psycho Pirate. Given their seniority, it's possible many of the Golden Age heroes adversaries either died, retired, reformed or went underground.

This is more of a post-crisis one, but another I just thought of is Prof. Ivo and T.O. Morrow