Here is a list of the Ministry's main departments as mentioned in the books. The employees listed for each office are the only ones we know of.

Minister of Magic : Cornelius Fudge

Department of International Cooperation

* Head: Bartemius Crouch senior (deceased)
* Employees: Percy Weasley
* Helped organize the Quidditch World Cup and the Triwizard Tournament
* Keeps up ties between Britian and other wizarding countries

Misuse of Muggle Artifacts Office

* Head: Arthur Weasley
* Employees: Perkins
* Responds to problems concerning enchanted Muggle items

Goblin Liaison Office

* Head: Cuthbert Mockridge
* Employees: Unknown
* Handles goblin affairs
* Keeps up ties between wizards and goblins

Department for the Regulation and Control of Magical Creatures

* Head: Unknown
* Employees: Amos Diggory
* Disposes of dangerous creatures
* Oversees the purchase and care of magical creatures

Department of Magical Games and Sports

* Head: Ludovic “Ludo” Bagman
* Employees: Unknown
* Handles the affairs of magical sports

Council of Magic Law

* Head: Unknown
* Employees: Unknown
* The wizarding world's judiciary system; a court of witches and wizards that judge over crimes committed by wizards

Improper Use of Magic Office

* Head: Unknown
* Employees: Mafalda Hopkirk
* Monitors illegal or unlawful use of magic

Committee on Experimental Charms

* Head: Unknown
* Employees: Gilbert Wimple
* Responds to accidental use of harmful magic

Accidental Magic Reversal Squad

* Head: Unknown
* Employees: Unknown
* Responds to accidentally reversed spells
* Modifies the memories of Muggles who have witnessed magic

Department of Magical Transportation

* Head: Unknown
* Employees: Unknown
* Sets up Portkeys
* In charge of Apparating tests
* Sets regulations for the use of broomsticks, enchanted vehicles, etc.

Department of Mysteries

* Head: Unknown
* Employees: Bode, Croaker
* Purpose is unknown