Hand to: Joffrey Baratheon
Tywin is no newbie to being Hand of the King — he was Aerys Targaryen's Hand, which was no small task. He's ruthless, clever, and fearless, employing whatever means necessary to accomplish what he believes should be done for the good of the realm (which usually ends up being very beneficial for his family, too). This includes trying to marry two of his children off to Loras Tyrell and Sansa Stark, not to mention orchestrating the Red Wedding. Ugh. For however unflinching and unpleasant Tywin was, he did bring one thing to the table that everyone enjoyed: he took none of Joffrey's whiny nonsense. At one point Tywin even sends Joffrey to bed without supper. That's ballsy, considering Joffrey once killed a prostitute with a freaking crossbow.
By the end of season four, Tywin serves as Hand of the King to Tommen after Joffrey is poisoned and proves that he gives exactly zero f*cks about his youngest son being wrongly accused of the regicide. Even though he is appointed to preside over the trial by Tommen, Tywin still sentences Tyrion to death. You can only push someone so much, and Tyrion takes out his father with a crossbow as he sits on the toilet. A satisfying but rather undignified way for such a towering figure to die, whatever his (admittedly major) personality flaws.