There are similar entities set up for other countries, though there appears to be little interaction between them.  We do meet some of the counterparts from the Bulgarian Government when the Quidditch World Cup is held in England between Bulgaria and Ireland.  The following departments, committees and offices are specifically mentioned in the text, or have to exist based on other facts specified.

Ministry of Magic - Cornelius Fudge
Department of Magical Law Enforcement - IV-526
    Misuse of Muggle Artifacts Office - Arthur Weasley IV-36
         Registry of Proscribed Charmable Objects - IV-91
    Accidental Magic Reversal Squad
       Obliviator - Arnold Peasegood
    Committee on Experimental Charms - Gilbert Wimple IV-86
    Office of Misinformation FB-xx
Department of Mysteries
     Unspeakables (Bode and Crocker) IV-86
Department of International Magical Cooperation - Barty Crouch - Percy Weasley, clerk
Department of Magical Games and Sports - Formed in 1750 - Ludo Bagman
    Tri-Wizard Cup
    Quidditch
          World Cup Committee
          There are 13 Professional Quidditch Clubs
             Wimbourne Wasps
             Chuddley Cannons
Department of Magical Transportation IV-66
         Floo Regulation Panel
         Bureau of Apparation Licensing -
Department for the Regulation and Control of Magical  Creatures - Amos Diggery
    Beast Division FB-xii
         Committee for the Disposal of Dangerous Creatures - III-218
         Centaur Liaison Office  FB-xiii
         Dragon Research and Restraint Bureau  FB-vi
         Licencing Bureau FB-9
            Crups
            Fwoopers
            Kneazles
         Pest Sub-Division - FB-7
    Being Division FB-xii
         Improper Use of Magic - IV-159
         Office for House-Elf Relocation - MB-vi
         Goblin Liaison Office - Cuthbert Mockridge IV-86
    Spirit Division FB-xii
         Ghoul Task Force FB-18

Council  of Magical Law - A Tribunal or court for determining innocence or guilt associated with breaking the laws.  IV-592

International Confederation of Wizards -

International Code of Wizarding Secrecy - IV-482
    Clause 73 - Each wizarding governing body will be responsible for the concealment, care, and control of all magical beasts, beings, and sprits dwelling within its territory's borders.  Should any such creature cause harm to, or draw the notice of, the Muggle community, that nation's wizarding governing body will be subject to discipline by the International Confederation of Wizards. FB-xvi

Code of Wand Use
    Clause 3 - No non-human creature is permitted to carry or use a wand.  IV-132
 

    Unforgivable Curses - Normally punished by a Life Sentence to Azkaban
       Imperius Curse - Imperio - Control of the individual victim. IV-212
       Cruciatus Curse - Crucio - Pain to the victim.  IV-213
       Killing Curse - Avada Kedavra - Instant death.

Dragon breeding was outlawed by the Warlock's Convention of 1709.

Ban on Experimental Breeding - FB-vi

Werewolf Register- FB-vi

International Ban on Dueling - Treaty not yet signed by Transylvania. IV-425

Decree for the Restriction of Underage Wizardry - II-81 - We know that Students at Hogwarts are not allowed to use magic when not at school or on their way to school on the Hogwarts Express.