Dany (who got her hands on the Iron Throne) had a son with Victarion, who she then put on the Throne of the Iron Isles (who were still independent), then she died in an accident...not a suspicious one, briefly uniting the Kingdoms under him but he died thirteen days later in a wild dragon's flames. The Kingdoms split again, with Loras ending up on the Iron throne and being labelled Oath Breaker because of his whole, Kingsguard thing. The Greyjoys got the Iron Isles back.
Not all that strange, admittedly, but I'm playing as the Blackwater Dynasty (beginning with Bronn) and my current character is married to the bastard daughter of Jon Snow, when the current Queen of the Iron throne dies a 'Cuy' will be on the Iron Throne...they're apparently Count level Lords.
The whole playthrough seems strange really. Templetons have the Riverlands, the Frey's have the Westerlands, Glovers have the North, the Royces have the Vale, Dragonstone has had a a dozen rulers because Dany kept giving it out and then revoking it over and over due to the event about her birth right. The Stormlands have a random family that was generated. Oh Rolly the Duck was a priest, on the baron tier, and the Warden of the South....that's kind of weird.
Oh and my son, due to being the son of the bastard daughter of Jon, is set to inherit Longclaw...he already wields The Monarchist and I wield Black Death...so he should have three swords by the end of it all...which is, you know, a little bit odd for the third generation of Blackwater. True, two of them are one's I've hunted down through events but I think The Old Bear wouldn't be too happy about a Blackwater wielding Longclaw.
If all goes to plan the Blackwater's should control three Valyrian Swords, be Lord Paramount of the North, while maintaining the Duchy of Rosby during the next generation...especially since the Glovers are waging war on the Throne and undoubtedly are going to find themselves without heads, eyes or genitalia very shortly.
Oh and a 42 year old Rickon with a Direwolf is master at arms for Skagos....would've thought he'd have come out of hiding by now...Oh and Brandon was a master warrior and a master at arms himself before his death...also hadn't come out of hiding. (Obviously there's no event for such a thing unless someone particular finds them, which seems slightly odd.)
EDIT: Excluding the independant Iron Isles, 50 years into gameplay not a single Lord Paramount is the canon family. In 50 years what has been the status quo for hundreds of years has been undone. Blackwater Dynasty now hold The North (didn't inherit longclaw, Sansa Stark got that), Fawcett's hold Westerlands, Winters hold the Reach, Tarth holds the Stormlands, Cuy's have the iron throne and Dorne (different people though)...forgotten their name...the family with all the bells on their COA...i know Bell is in their name somewhere...well they have the Vale..and the templeton's still hold the river lands, which I realised came through the claim of Sansa Stark, their mother.
Long story short, all of the 'major' houses are now all but extinct, the Manderlys are gone, the Karstark's have one living member, who doesn't hold Karhold, the Starks will die with Sansa, unless Rickon outs himself, the Lannister's are plentyful but only hold two counties in very different branches, the main branch of Arryn is dead, Royce is dead, Tyrells have vanished and so on. The only absolutely constant families are the Clansmen in the North of the North, the Mormonts, the Thenns and the King Beyond the Wall, who has reigned (almost) peacefully for some thirty years.
Not very 'crazy' but considering the Starks, Lannisters, Arryns, Tyrells, Tullys and Martels have been at the forefront for generations the fact that they're all now more or less powerless is kind of WTF...no?...okay so with the starting point the Starks, Arryns and Tullys were all but gone anyway but the others probably should not have been outlasted by the Greyjoys really...