Not referring to law enforcement agencies:
In the US there are 16 agencies (watch this 2 min video). The more widely known are the National Security Agency (NSA), The Central Intelligence Agency (CIA), The Department of Homeland Security (DHS), and The Directorate of National Intelligence (DNI).
In Israel Mossad is the main agency, along with Aman and Shin Bet.
The Chinese Communist Party (CCP) has an intelligence wing within their People’s Liberation Army (PLA)
In the United Kingdom (UK) the main organizations are the Secret Intelligence Service (SIS or MI6), the Security Service (MI5), the Government Communications Headquarters (GCHQ) and Defence Intelligence (DI).
The KGB existed in the Soviet Union from 1953 to 1991 when it was disbanded. Today Russia operates a Foreign Intelligence Service.