Why do I have a feeling that Tywin was the head of the plot on Joffrey?
He has the most to gain. Remove a tyrannical king that would surely have the kingdom fall when winter hit, let alone the invasion of Daenerys. Joffrey being king would destroy the kingdom and the family.
He get's to install and groom someone who is clearly easy to manipulate and extremely passive. He will basically be king while Tommen is alive.
Littlefinger was in on it, but what does he have to gain? Nothing that I can think of.
Varys is the only one who I wonder about. He knew about what was going down. He was trying to get Shae out of town before it went down. If I recall correctly he was also trying to get Sansa out too, knowing that she would be the key factor for the set up.
Just look at him during the wedding. He knew what was about to go down, and even though he knew what a cunt Joffrey was, having Sansa be one of the fall guys may not have been doing good things with his conscious.
Tywin knows what's up. While he's doing everything for the sake of the family name he has to get the kingdom together before winter and Daenerys hit. He's getting everything into motion to take control and stabilize the situation that Joffrey created.
EDIT: Also, what the fuck. A whole season of making Jamie sympathetic and they blew it all up. However, we must remember that he's a fucking horrible person. He threw a kid off a tower, he's not a good person, but that doesn't mean we can't witness his struggles and sympathize with them to a degree.