Gotham City Police Department (GCPD)
The Gotham City Police Department is the main law enforcement agency in Gotham. Brutal, uncompromising, and corrupt, the officers of the GCPD are confronted by low budgets, rampant street crime, and immensely powerful criminal organisations. The rank and file try their best to get by, taking in a little extra cash on the side. The higher-ups too are corrupt, an are often in the pockets of the criminals or unscrupulous politicians. Some police officers are known for taking on assassination contracts and gang killings. Many of the police are little better than the people they purportedly are after.
Gillian Loeb is the current police commissioner.
Federal Bureau of Investigation, Gotham City Division
The FBI is the a federal law enforcement organisation with offices in every major city in the USA. It's agents are well-equipped, excellently trained, and known for having far greater resources than any city PD. Naturally in Gotham this means that many inside the GCPD detest the "Feds".
Their superior is Special Agent Eric Forster.
International Guard, Unit 84 (IG-84)
The International Guard is a worldwide mercenary group based in Berlin, led by former Israeli Army Colonel Avram Kleinman. Each of the units around the world have a number designation. Gotham's unit, unit 84, is led by a Northern Irish officer called Tom Carson. A former British Army member with years of combat under his belt, he now leads his group of men in the name of the almighty dollar.
Their commander is Major Tom Carson.
Maroni Family
One of Gotham's major mafia families, the Maroni Family is led by Salvatore Maroni, a hot-headed boss who is known for his use of car bombs in his attacks. His organisation has major interests in drug dealing, contract killing, robbery, and extortion.
Falcone Family
The greatest of the "Big Four" of Gotham's Mafia families, the Falcones rule the underworld of Gotham with an iron fist inside a velvet glove. Carmine Falcone, the "Godfather of Gotham", has formed a network of alliances with the smaller criminal gangs in the city that enable the Family immense power and allows them to resolve many disputes without resorting to war. Politicians, cops, attorneys- Falcone owns them all. Or most of them, anyway. The Falcones control waste management, prostitution, gun running, hijacking, vote rigging, and myriad other crimes.
Caruzzo Family
Second in power and influence only to the Falcones, the Caruzzo Family are known to be the most secretive of the Big Four Italian American mob families in Gotham. Little is known about their leadership or strategies. The don of the family, Francis "Frank" Caruzzo, is known as the "Invisible Don". The Caruzzos main interests are gunrunning, contract killing, bank robberies, extortion, intimidation, and political corruption. The Caruzzos are closely allied with the Falcone Family. The Caruzzo Family have a dedicated hit team known as the "Headhunters" that have become part of Gotham's urban legend.
Marcelli Family
The smallest of the Big Four mob families, the Marcelli's are known as the drug pushers of the mob. Violent and unpredictable, the Marcellis are almost constantly in a low-intensity war with the Russian Bratva in Gotham. They are led by Ercoli Ruggerio, who took over the family after Luigi Marcelli was killed by a Caruzzo made man one year ago.
Bratva
The Russian Bratva is a very aggressive, very bloody criminal organization that is heavily involved in drug dealing, prostitution, and pornography. They have no fear of the police, and many of their members are "un-arrestable", meaning that they will fight to the death rather than be apprehended.
This is not a complete list; feel free to give me any ideas or suggestions.