I think it's time the career of Ser Gregor Clegane was re-evaluated. I've heard it suggested that he's a victim of circumstance, but so many of his actions seem like they must be deliberate. But why are Gregor's actions so over-the-top and brutal? Won't they damage Tywin's reputation? We know Gregor was a promising young squire, knighted by Rhaegar himself, so how did he come to be such a monster? The answer is simple: Gregor Clegane is a double agent working for the Tullys to discredit the Lannisters.
Gregor was recruited by Hoster Tully at an early age, after the marriage alliance between Catelyn and Jaime fell through. Hoster knew he couldn't rely on Tywin in future, so made an effort to get a man on the inside of Tywin's operation. The Cleganes were known as a loyal house and Gregor looked like he would develop into a great fighter, so Gregor was a good choice. Gregor would make himself invaluable to Tywin, and meanwhile do everything in his power to undermine the Lannisters and help the Tullys. In exchange, Hoster promised to protect Gregor's beloved sister, who was being abused by their cruel father. Hoster arranged for the Clegane girl to be spirited away to safety and a new identity, covering it up as a death. He and Gregor also worked together to dispose of Gregor's father.
Gregor's first big mission for the Tullys came in Robert's Rebellion. When he realised that Tywin was to join the rebels, he knew he had to make sure that the Lannisters weren't in a position to take over the kingdom. So when given orders to storm the Red Keep, he deliberately undermined Tywin's moral authority by misinterpreting his orders and raping and killing Elia, despite there being no order. He knew this was likely to enrage Ned Stark, who would be first on the scene, and deprive the Lannisters of a good bargaining position. In fact, Robert forgave Tywin, but Ned never did, helping ensure he would side with the Tullys in future.
At the start of the War of the Five Kings, Gregor is “set loose” on the Riverlands by Tywin, and raids a number of towns and villages. This gives the Riverlords an opportunity to travel to King's Landing and, in full view of the court and the king, expose Tywin Lannister's villainy. Unfortunately, it's not Robert who hears the news but Ned, but it still helps to turn the minds of those present towards the threat presented by the Lannisters.
When Gregor discovers that the force sent by Ned is not commanded by Ned himself, he realises that if he attacks the king's banner, this will make Tywin a rebel and answerable to the king's authority. He attacks Beric as publicly and graphically as possible, making sure that everyone hears about it. Unfortunately, events overtake him, and Robert dies before he can retaliate. The Lannisters are now in a much more powerful position, and Gregor has to rely on his own efforts, rather than just doing things to disgrace Tywin publicly.
At the Battle of the Green Fork, Tywin gives Gregor command of the vanguard and the left flank. Tywin's intention is for the vanguard to be overrun, so he can spring a trap, but Gregor selflessly ruins this plan by winning his area of the field and persuading the northmen to withdraw. This deprives Tywin of a decisive victory and allows Roose Bolton to remain as a thorn in Tywin's side.
When given his own command, Gregor heads straight to Castle Darry, held by a family who led the resistance to Hoster Tully during Robert's Rebellion. Under the guise of a Lannister atrocity, Gregor sacks the castle to punish the family for their past transgressions against his Tully masters. After this, Gregor continues to rampage around the Riverlands, ensuring that the local lords are increasingly dependent on Riverrun and the Tullys for their defence and security.
Tywin then recalls Gregor for his assault on the Stone Mill. Gregor has worked out Robb's plan, but doesn't know if Hoster has told Edmure about his double agency, and doubts whether any messages he sends will be believed. Instead, he decides to do his best to make sure Robb's plan succeeds, and so strives more than any of Tywin's other commanders to force a crossing. When he realises this is impossible, he ensures the Lannister army suffers heavy casualties in retreat to weaken Tywin further.
Gregor's next target is Roose Bolton. He knows Roose has been planning to betray the Starks and Tullys, thanks to his spies in Harrenhal, and wants to eliminate him before he can do any damage. Unfortunately, at the Ruby Ford, Roose is able to escape Gregor before he can bring him to justice. Enraged that Roose has eluded him, Gregor takes it out on Roose's followers at Harrenhal, although he makes sure the captive loyal Northmen are well-fed on roast goat.
In his final act, Gregor is recalled to Kings Landing to stand as champion against Oberyn Martell. Gregor does his best to annoy Oberyn publicly by feigning ignorance of his past crimes, ensuring that Oberyn declares them loudly for all to hear. Then Gregor finally confesses his guilt, knowing that Westeros will judge Tywin for the crime rather than him. Finally, he kills Oberyn so that Tyrion remains locked up, depriving the Lannisters of a useful brain, and driving a wedge through their family unity.
It remains to be seen whether Robert Strong retains his former allegiances and memories, and whether he will take a dive in Cersei's trial by combat. Overall, though, I think it's clear that Gregor is probably the most underappreciated, arguably even the greatest, hero of Westeros in modern times. The full litany of his deeds will probably never come to light, since the Tullys are all but gone and it's in their interests for Gregor's actions on their behalf to remain unknown but it would be nice to think that in a hundred years' time there could be a statue, or town named after him, in the Riverlands, commemorating all he did for them.