Stannis Baratheon. Stannis (Stephen Dillane) is the rightful king following the death of his brother Robert. Beyond that, he also seems to be the only person who cares about the kingdom more than his own power. He just saved the North by wiping out the Wildling threat without any clear benefit to himself, and we get the feeling he’d be a just ruler. Flashy, no, but just.
Tommen Baratheon. Tommen Baratheon (Dean-Charles Chapman) is already king, and he’s way better than Joffrey, so why not just leave him in command? We know, he’s a product of incest and all that, but if everyone got to know him, they’d see that he’s a nice kid with the potential to be a great king.
Jon Snow. Jon Snow's (Kit Harington) odds of becoming king are admittedly slim, thanks to his bastard blood and Night’s Watch vows, but that doesn’t mean we can’t dream. Jon has proven himself to be a great leader with a good heart who’s able to make difficult decisions, and he may be the only one on this list who takes the White Walker threat seriously.
Tyrion Lannister. We’ve already seen Tyrion's (Peter Dinklage) leadership qualities when he saved King’s Landing against Stannis’ invasion during the Battle of Blackwater, which highlights Tyrion’s chief advantage among his peers: his intelligence. Tyrion is smarter than pretty much anyone in the Seven Kingdoms, and his brains should be able to figure out how to peacefully run the country. His stock may have taken a hit after murdering his girlfriend and father, but he had his reasons.
Margaery Tyrell. King’s Landing, and Westeros in general, is made up mostly of poor peasants. The show focuses mostly on the wealthy noble houses, but most of the population is dirt poor. So far, the only character who seems conscious of their plight is Margaery (Natalie Dormer). While it’s possible, and even likely, that her crusade for the poor is done mainly for political reasons, she’s still the only one talking about them.
Who do you think should sit the Iron Throne?