The world's foremost superhero team is the Justice League of America. Often referred to as the Justice League or simply the JLA, my incarnation aims to incorporate the classical line-up as much as possible. As of 2010, the JLA consists of Aquaman* (King Orin of Atlantis/Arthur Curry), Batman (Bruce Wayne), The Flash (Wallace 'Wally' West), Green Arrow (Oliver Queen), Green Lantern* (John Stewart), Hawkgirl* (Shayera Hall), Martian Manhunter (J'onn J'onzz), Superman (Clark Kent/Kal-El) and Wonder Woman (Princess Diana of Themyscira). There are dozens of part-time, associate and reserve members (including the staff and students of the Justice League Academy) but those listed are the primary, standing roster. The Justice League is headquartered at The Hall of Justice (located in Metropolis) or their orbital space station known as "The Watchtower".
The second most prominent team is the Justice Society of America. The JSA are one part superteam, one part social club and help train those legacy heroes descended from their various Golden Age members. Currently the older members are referred to as the Justice Society while the younger, newer members are often called the Young All-Stars or (as they themselves prefer) The All-Star Squadron*. Current membership includes Atom Smasher* (Grant Albert Emmerson), Cyclone (Maxine Hunkel), Dr. Midnight (Pieter Anton Cross), The Flash (Jay Garrick), Green Lantern (Alan Scott), Hawkman* (Carter Hall), Hourman (Rick Tyler), Liberty Belle (Jesse Chambers), Mr. Terrific (Michael Holt), Power Girl (Karen Starr/Kara Zor-El), Stargirl (Courtney Whitmore) and Wildcat (Ted Grant). Associate and other allied members exist but I'm focusing this team being a bit smaller than it often appears in the comics these days. The team is based out of New York City.
No list of DC Universe superteams would be complete without the Teen Titans, who are among my personal favorites when done well (which hasn't always been the case sadly). The main difference between the Titans and our version of Young Justice is age; The Teen Titans are roughly high school age (13-19) for the most part while Young Justice is a roughly college age group (20-26). The other major difference is that the connection between the Titans is one of family, even if that family is largely dysfunctional. The current Teen Titans of Earth Alpha D-1 are Kid Flash (Bart Allen), Miss Martian (M'gann M'orzz/Megan Morse), Robin (Tim Drake-Wayne), Speedy* (Cissie King-Jones), Superboy (Conner Kent/Con-El) and Wonder Girl (Cassie Sandmark). The team is lead/mentored by former Titans Cyborg (Victor Stone), Changeling (Garfield "Beast Boy" Logan) and Raven. The number of allied members are far too numerous to recount here. Titans Tower, the group's distinctive headquarters, is located in San Francisco Bay.
Whew, that's enough for now. Next up we'll look at the independant heroes, those characters and teams that are significantly altered from their comic book counterparts and maybe...just maybe...the PCs of Justice League Academy.
A note regarding those names with an asterisk " * ". Characters so noted are slightly different from their current DC universe incarnation but essentially recognizable to even the most casual fan. I have, in these cases, chosen the best possible take on the character or combined multiple incarnations to come up with a version that works for this campaign. For example, on Earth Alpha D-1, Green Lantern John Stewart looks and acts like the Justice League Unlimited animated series version instead of the sad sack version normally portrayed in print.