The Brotherhood of Evil was founded years ago by The Brain, who is actually a disembodied human brain preserved in a special fluid. They have batted the original Doom Patrol numerous times until Madame Rouge was driven insane after one of the Brain's experimental surgical operations. She turned on her comrades with another Doom Patrol foe called General Zahl and tried to kill them.
With Madame Rougue's daughter, Gemini, joining the team, who were reunited by Phobia, Mallah, and the Brian, they joined the Society. Under the command of inner circle member Deathstroke the Terminator, they used Chemo to bomb
Blüdhaven and murdered several million people in the process. They became the most wanted villains in the DC Universe for their mass murder.
One Year Later
The Brotherhood returns their original roots with the addition of two new members after loosing Phobia; The Elephant Man and Goldilocks. They launched massive crime waves of the remains of the Secret Society. Their goal included cloning a new body for their leader as well as creating unstable clones of active super-heroes to sell to third world dictators, putting them in conflicts with the Teen Titans, Doom Patrol, and the Outsiders.
The Briain, Monsieur Mallah, General Immortus, Phobia, Plasmus were later seen in Salvation Run. While on the Hell Planet some of the members have been murdered one by one. The Brain and Mallah were killed by Gorilla Grodd, and towards the end of the event General Immortus was 'killed' during a battle with Parademons (he is later revealed to be alive and well, and has formed a new team, The Army of Endangered, in Final Crisis: Run) and Plasmus and Warp were used in Lex Luthor as a source of power for a teleportation device as they and a few others were seemingly killed when it self-destructed. What remains for the future for this organization remains to be seen.
In Teen Titans Go! #48, there is an alternate version of the Brotherhood of Evil called the Brotherhood of Justice, who fight against the evil version of the Teen Titans called the Teen Tyrants. This team consists of Dr. Light (the Kimiyo Hoshi version), Mammoth, Madame Rouge and Psimon (who is nearly similar to Brainiac).
A renamed group formed by the Brain and Mallah called itself the Society of Sin.
In Other Media
The Brotherhood of Evil appears in SEASON 5 of Teen Titans. In this version, they are made up of four members, considered to be an elite evil that has been working for countless years, fighting its nemesis the Doom Patrol (Mento, Elasti-Girl, Negative Man, Robotman & Beast Boy).
They have "slept" for some time, in a time of inactivity on their part after their defeat by the Doom Patrol.
But they rise again and it is only when Beast Boy binds together his former teammates from the Doom Patrol and current teammates from the Teen Titans that the Brotherhood is defeated.
They then recruit almost every single villain ever seen in the Animated Series with the single purpose of eliminating ALL the Teen Titans.
So it is that in a final battle they send their servants out to kidnap Teen Titans so that they may be flash-frozen:
Robin is captured by Madame Rouge.
Thunder is captured by Steamroller and the I.N.S.T.I.G.A.T.O.R.
Lightning is captured by Overload.
Aqualad is defeated by Plasmus and Trident.
Tramm defeats XL Terrestrial but falls alongside Aqualad.
Speedy is captured by Cheshire
Hot Spot is deceived and captured by Madame Rouge
Wildebeest is captured by Madame Rouge.
Menos is captured by Johnny Rancid and Cinderblock.
Killowat is captured by Control Freak and Puppet King.
Argent is captured by General Immortus by him using his robots.
Bushido is defeated and captured by Katarou.
But the Titans all band together into four teams under the leadership of Beast Boy (Más, Herald, Jericho and Pantha), Cyborg (Kole and Gnarrk), Raven (Melvin, Timmy Tantrum, Teether and Bobby) and Starfire (Bumblebee and Red Star) along with the vigilante heroes Kid Flash and Jinx.
They proceed to free Robin and the captured Titans and so the Brotherhood is defeated and left to suffer to the horrible fate they had provided access to, so they are flash-frozen.