Well frankly, I knew they were trouble from the start. Of course, considering their house colours of crimson and gold, one would expect them to do no less than conspire, plot, murder and scheme for riches.
Though I can see Tywin Lannister's natural claim to the castle of Harrenhal. It's dark, mysterious and massive, just like him. Compliments to him for being so badass and admirable at the same time.
And Tyrion, with his cunning and egoistic ways, manages to be my favorite Lannister. But the Kingslayer has some merit. After all, Jaime is a skilled swordsman. And while pondering on that, Cersei is quite a character herself. Strong-willed, mean and ruthless (gets you wondering how she spawned Joffrey)
As for Myrcella and Tommen, well, there's more to be read about them.
Lannisters of Casterly Rock
Here Me Roar!