They even gave a bit of humanity to Joffrey this last episode.
Of course Tyrion is the ultimate amoral ******* you can't help but root for.
I don't know if I'd say that much about Tyrion. He's a complicated character, without a doubt.
His dwarfism makes him an oddity, since life in Westeros is so hard that a child with birth defects would ordinarily be left to die. But since he's a Lannister he's had the benefit of the best of care due to the family's riches. But in contrast, he's always had the disdain of his own father since Tyrion's mother died giving birth to him. And Tywin won't seem to forgive Tyrion for that. And his siblings are near perfect, which makes Tyrion that much more of an outcast. Tyrion's personal moral failings seem to be an exercise in him seeking refuge and comfort since he gets next to none from his family.
Where Tyrion really seems to show his character is in the dealings with the other House of the Seven Kingdoms. When it comes to dealing with the Starks, he's been very honorable. He acted very much as a good counsel to Jon Snow when he rode up to The Wall. He chastised Joffrey for not showing proper courtesy to Catelyn Stark following Bran's fall. And he was one of the few people to comfort Sansa Stark following Ned's execution at Joffrey's hands.
Tyrion has the makings of a statesman, but a terrible personal life. Of the three Lannister children, I think that only he would be a proper heir to Casterly Rock. But Tywin's grudge against him has clearly stood in the way of him leading the Lannister house.