Ok, I will hopefully contribute a bit to the thread myself, the thread is one of my favourites surely. Most of them are from 1.06/1.06b.
I will start with a couple rare culture/religion/government type combinations, created by AI. Some of them have been seen already, but nevermind.
Doge Abu of Algaid republic. I don't remember the story behind this, but it seems he held a bunch of republics in the southern Italy. Capital in Mallorca.
Theocracy in Scotland. Dynasty map mode. IIRC the Theocracy lasted over a century.
Badshah Ruprecht. The HRE went Rommel and the Kaiser had his capital in somewhere in Tunis. His heir culture flipped to Maghreb. Needless to say, when he inherited, the HRE exploded.
My kinsman Martin, Occitan Yazidi Emir who had some crusading history. I think I won a crusade, gave the lands to my relatives, who were conquered by heretical Muslims afterwards.
France gone Sunni.
A Breton Caliph, King of Sicily, lands in Bretagne and in two corners of Iberia.
Yeah, old stuff but still interesting. I think this will be very rare in 1.07, judging by the changelog.
More to come.