Well, I let my characters' personalities inform the outcomes of that. (I beat the game with both of them.)
Spoiler Below My dwarf commoner rogue was fiercely loyal to the Wardens and his friends, particularly Alistair. He was also a pragmatist so he would have considered letting Loghain join, but given his crimes against the Wardens and Alistair's insistence that he die for them, he let Alistair kill him. For similar reasons he let Anora take the throne-- he didn't really give a **** about Denerim as a kingdom, and being a commoner, certainly not about bloodlines. He would much rather make his friend Alistair happy and give the kingdom a leader strong enough to turn back the blight.
My elven mage on the other hand was more of a moralist. She distrusted and disliked Anora, who had betrayed her- I managed to kill Ser Cauthrien instead of being arrested-- and made Alistair take the throne. Loghain of course had to be punished for his crimes, and my character was again close to Alistair, so she also had Loghain killed.
I have plans for an amoral bastard of a third character, a human noble warrior. He'll probably spare Loghain, not give a **** about Alistair, and... if possible take the throne for himself. Otherwise, eh, I dunno, I'll have to see. I'm giving the game a good long rest before I go through it again.