Someone suggested that I separate my theories blog into separate posts by subject. If you're looking for the blog post with complete theories, it's still here.
I think that Roderic Calanthis is most likely the king Kvothe kills. When Kvothe was helping to prove to the Maer that he was being poisoned, he sacrificed sipquicks (also known as Calanthis) in order to protect the Maer. Personally, I think that was foreshadowing to Kvothe killing King Calanthis to protect the Maer. I think the Maer will abjure his actions in an attempt to not be seen as a conspirator, which would explain Kvothe's contempt for the Penitent King. If the previous king was killed by someone who is associated with the Maer, that would also explain the unrest, as well as the title of "Penitent King". Given that the soldiers travelling through Newarre wear the Maer's colors (despite not being in his lands), I think that this is the most likely.
Sometimes I hope that the king Kvothe killed is Ambrose, but I also think that's what Rothfuss expects us to think, so it probably won't be. I think there's also a chance that he's the penitent king. He has a lot to pay penance for, and it would explain why Kvothe was so horrified by the idea of toasting to the Penitent king (though there could easily be other explanations as well).
I'm wondering about Vashet's "poet king". While a large part of me is hoping that it's just a red herring (because that large part of me wants Kvothe to have gotten his name of Kingkiller, and his sword's name of the Poet Killer, by killing Ambrose), I wonder if her "poet king" is instead the one he kills. She mentioned him enough times that I think he'll be important somehow.
I've heard people theorize that Simmon will be the king Kvothe kills, but it's mentioned more than once that he's terribly far down the line, and I can't see anything that would bring Kvothe to kill him.