To clarify, my primary curiosity is with the evolution of espionage as a whole. Centralized modern states are relatively new inventions, so it stands to reason that the intelligence services of such states are also relatively new developments. Elizabeth II has MI6, but what did Elizabeth I have?
The CIA was preceded by the OSS, or the Office of Strategic Services. The OSS was a wartime agency that mostly dealt with wartime affairs, but the CIA changed that when it replaced the OSS at the end of World War 2. The CIA became a domestic and international agency, both civilian and war focused, and today focuses mainly on anti-terrorism. The KGB's origins date as far back as the Russian Revolution, starting with the name "Cheka" and helping with the revolution. It partook in The Great Purge under Stalin in 1936 under the name of NKVD and that specific organization lasted until Stalin's Death in 1953. It was then finally replaced by the KGB under Khrushchev, who purged the Head of the "State Security" (NKVD) in fear of a coup. After Khrushchev purged the NKVD of all Stalinist sympathizers, it was finally christened the KGB. The KGB lasted until 1991 with the fall of the Soviet Union. The CIA, of course, lasts to this day.