In Star Wars, the events of Order 66 can be laid to rest at the feet of a number of individuals. Darth Sidious would be the most prominent one, given that he orchestrated a galaxy-spanning conflict for that purpose, and Darth Vader would be another, given that he was the one who ransacked the Jedi Temple and helped the Dark Lord of the Sith accomplish that task. But there were a number of signs pointing towards it beforehand, some of which were ignored by the Jedi, including the Grandmaster of the Order himself, Master Yoda.
A prominent example of this comes from The Clone Wars: Stories of Light and Dark. The first story in the collection, "Sharing the Same Face" by Jason Fry, follows the events of the Clone Wars episode "Ambush," and provides details that weren't present in the episode proper. One particular scene comes after the episode when Yoda uses the Force to get a sense of the Clones he had worked with. When he does this to Thire, he received a vision.
"And he saw Thire, in a helmet with bright crimson flares. He was searching for something. And with him was another presence -- one that felt like a vast storm in the Force, full of malice and greed."
For those unaware, Thire was one of the Clones who searched for Yoda after his duel with Palpatine in Revenge of the Sith and later escorted Palpatine to Mustafar after Darth Vader's duel with Obi-Wan. Yoda sees a vision of his own future when Darth Sidious has declared himself Emperor. The person Thire is hunting in that vision is the Jedi Grandmaster himself.
Despite this massive clue, Yoda chooses not to follow up on this, despite the clear implications of horrible events that would occur. Yoda believed that predicting the future was dangerous and taking steps in trying to prevent it may end up causing the very future he was trying to stop. An understandable sentiment, especially given Anakin Skywalker's own efforts did the exact same thing later on down the line. But at the same time, Ahsoka Tano also showed that acting on visions like those could very well prevent it, as Ahsoka did when she got a vision of Padme Amidala being assassinated by Aurra Sing and took steps to prevent it from happening.
Yoda should know this, as she confided in him about her vision, yet not once did the Jedi Master consider doing the same with his own vision. Furthermore, Thire went to go on and work directly for the Chancellor himself, which should have given Yoda a clue that Palpatine was the evil force Thire was serving in that vision.
If Yoda had followed up on that vision and chosen to look more closely at what he saw in Thire's future, Yoda may very well have been able to figure out who Palpatine really was and prevent the events of Order 66 from ever occurring at all.