I had a run where I played as Joff, then Tommen, then Tywin, and finally Tyrion. Joffrey gets assassinated and Tommen becomes king. Lancel decides to be a maester. Literally the day after he returns from the Citadel, Aegon sacks KL, and for some hilarious reason decides to instantly execute Lancel. Jaime, Cersei and Tommen are all eventually executed, and I (now as Tywin) declare war on the Iron Throne to rescue Tyrion. I fail miserably, and when Aegon demands I surrender, I declare myself King of the Rock, and weirdly that prompts Aegon to give me Tyrion back for nothing in return. He eventually sacks the Rock though, and I die in the dungeons. And then no one wants to marry poor Tyrion :(

Also a wildling is LC of the Watch; Margaery marries someone from the Plains of the Jogos Nhai; Victarion is Iron King after Balon dies in a duel and Theon succumbs to the pox; Dany is a lunatic and ruling in New Ghis despite being Aegon's queen; Varys becomes a lord and marries; Sandor killed Gregor; and Team Dorne is the only group that has survived entirely unscathed.

And Stannis somehow became best buds with Aegon!