Provided courtesy of Rexer. Please note that some of these units have been disbanded since the end of the Cold War.
Spetsnaz
The KGB had several small, elite, Spetsnaz units. The most known of these is the Alfa Group, or "Spetsgruppa A". Alfa group is no secret in Russia, but their operations are classified. Alfa Group was formed in 1974 as a part of the 7th (Surveillance) Directorate of the KGB with a counter-terrorist and crime fighting role. Alfa operators saw service in Afghanistan and Chechnya, as well as domestic operations. Today, it still exists as Alfa Group or Spetsgruppa A in the Russian Main Guards Administration.
Another KGB Spetsnaz unit was "Vympel" or "Pennant", created in 1981, and it was under the control of the 1st (Foreign Intelligence) Chief Directorate. The squad eventaully increased itself to reinforced battalion strength (about 500) was created as a diversionary special force for use behind enemy lines in case of war. It now exists as "Vega" in the Russian MVD.
Other lesser known, KGB Spetsnaz units included "Kaskad" (Cascade) in the 8th (Guard's) Directorate, "Zenit", "Grom" (Thunder), and "Spetsgruppa B".
Gosudarstvennaja Bezopasnost
Another specialized unit, dating from the days of the Cold War was specially assigned to guard nuclear weapons sites that were deemed too important to be guarded by the MVD. Their shoulder boards displayed the letters GB or 'Gosudarstvennaja Bezopasnost' in Russian. The color of the shoulder boards of the members of the "GB" are blue. Not the the sky-blue like the ones of Paratroopers or Aviators, but rather darker like a blue background on the American flag. Thanks to Igor for this info.
Demolitions Units
During the Cold War there were special KGB units trained in the use of atomic demolition munitions that would be attached to VDV, or Airborne in the event of war.