I can't believe that with so many RPers on the forums there are no SGs where they "do their thing". I'm sure that I won't be the only one benefitting from a list. So, let's follow the official format:
<ul type="square">[*]Group Name: [*]Server: [*]Contact Info: [*]Description:[/list]
Group Name: The Nemesis Council
Server: Virtue
Contact Info: http://www.realitywerks.com/phpbb/
Ingame Contact Info: Asper, Dire Moon, Zeromus, and of course myself as DrivenMad
Description: The Nemesis Council is exactly what it sounds like. A supergroup comprised of "Evil Characters". We also have a sister supergroup "The New Porter Institute" who are the "Good Guys" You can find more information to both groups at the link above.
Group Name: The Freedom Phalanx
Server: Champion
Contact Info: http://www.elementsunite.com or through private message on CoH forums to 'Stateswoman'
Ingame Contact Info: Stateswoman, Freedom Avenger, Federalist, Silverstreak
Description:
Today the Freedom Phalanx is the worlds premiere independent hero organization. They are one of the most open organizations in existence, allowing any would-be hero to volunteer for service with the esteemed group...
The Freedom Phalanx continues to rebuild and reform from the devestation of the Rikti War even as its selfless membership attempts to aid and support the rest of the world in doing so as well. Keeping with long time policy, young heroes are invited and welcomed to serve with the esteemed organization and its storied heroes throughout the world where ever there is need. In major cities around the globe, junior divisions of the world famous supergroup have formed to continue training under the supervision of senior members of the fellowship.
One such division has recently formed in Paragon City and is already acting under the supervision of the heroes known as 'the Surviving Eight', such as Positron, the Back Alley Brawler, and Numina. Led by Anna Anderson, a young hero from California also known as the Stateswoman, the burgeoning group has scored some impressive victories against the many villains who would do the great city harm.
OOC: The pacing of this group is a lot more casual than most of the larger more fast-moving/leveling supergroups, and was started as a alternate option for members of the Elements organization who are interested in roleplaying and staying in-character while playing along with the story content provided by the Devs. All roleplayers are very welcome to join, feel free to contact me at stateswoman@houston.rr.com and/or at Stateswoman on the official forums with any questions or interest you might have and leave an in-character note in the 'Interested in Joining' thread at the forums at http://www.elementsunite.com on as well!
The Sect <period>
and our Birthright Confederation
see links below...
A SG without comparison anywhere... <period>
Ordinary Citizens have heard the call. Gratitude is never enough!
Group Name: Citizens' Defense League
Server: Freedom
Contact Info: In-game email Dr. Maningzhoue, or PM me here.
Description: Still newly forming 1 late 30s, and another guy in his late 20s. Naturals as well as magic and tech origins who are still ordinary human beings. More at Citizens' Defense League (Edit: Incidentally, this means *you* katana/invuln, broadsword/invuln, and Martial Arts/Super Reflexes scrappers, and you, Assault Rifle/Device blasters. Not to mention human wizards and the powersuit set.)
Choosing a Controller V2 | Splattrollers | Plant/Rad | Fire/Storm | Mind/Emp & Mind/Rad
Weird Controller Powers | Conf & XP/Time | Controller Damage
Being a Healer | The word Necessary | Natural Concept Characters
Group Name: The Less Fortunate
Server: Infinty
Contact Info: Tick-Tok
We are a fairly new sg, not that many members bu we still have fun! we roleplay fairly often, and were always there to help! We except and levels and origins
There are tons of RP supergroups of all persuasions on Virtue. You can find some of them here:
Virtue Supergroups
For other servers, such as the one on which you are already active, you may wish to run a board search under the server forum for RP supergroups.
Infinity Supergroups
Good luck! 
I've been trying to find one that RPs and would fit my character. So far, I found the simians, the felines and the actors. None of them fit my character, for I am not a monkey, nor a cat, nor an actor.
If you run / know of other RPing SGs, please post them here, prefferably with contact info. I am on the Infinity server, but I am sure there are plenty of RPers who would appreciate a list.
Thanks.