Magocracy (Rule by Mages), Theocracy (Rule by Clergy), and even Kleptocracy (Rule by Thieves) are not uncommon in fantasy settings, but how about some rarer or more extreme governments you might find?
Dracocracy (Rule by Dragons) Crassusocracy (Rule by the Fattest) Bellacracy (Rule by the most Beautiful) Necrocracy (Rule by Ghosts) Deiocracy (Direct Rule by Gods) Dodecakirinocracy (Rule by People Chosen by 12 Kirin) Columnaevirumocracy (Rule by Women Esteemed by How High the Column upon which their Husbands Sit on Happens to Be)
reminds me of asimov's foundation (itself based on the sibylline books of rome)
Liam Williams
>Kleptocracy (Rule by Thieves) Name one time this happened in fantasy. also, I'm not sure it's supposed to mean "rule by thieves" in the sense of a thief upper class, but more in the sense of politicians who steal the resources and wealth of their nation. Kind of like modern Russia.
>Crassusocracy KEK! KEK!
Easton Morris
My favorite rare real-world government type is Kritarchy (rule by judges). It's generally not a very good government type, but it's interesting.
Isaac Brooks
The Tower of the Elephant, one of the more famous Conan stories, starts off in a city of thieves, and later stories influenced by this idea include cities ruled by a King or Prince of Thieves.
Asher Brown
Charismacracy (Rule by animal magnetism) Nanarchy (Rule by unthinking machines) Panarchy (Everyone is his own nation) Panocracy (Rule by totality, hive mind)
Luke Gonzalez
Lankhmar's Thieves Guild holds massive political clout, though it doesn't directly rule the city.
Grayson Mitchell
Orion's Arm?
Adrian Williams
>Crassusocracy (Rule by the Fattest) so like america :^)