When the clones are issued Order 66
telling them to turn on the Jedi,
do any of them refuse to carry out the order?
There's no evidence within the main film and TV canon of a clone trooper disobeying Order 66 (due to the fact that they were implanted with an "inhibitor chip" guaranteeing their loyalty).
Probably the closest we get is in the Clone Wars TV series where we meet a deserting Clone named Cut Lawquane. Since he's hiding from the Empire and supports the Jedi, I think we can reasonably assume that his chip is already damaged in some fashion and that he would have refused Order 66 if he received it.
Elsewhere in the book EU, we see in Dark Lord : The Rise of Darth Vader that not all of the clones obeyed Order 66. An entire squad went rogue due to their affection and personal loyalty to their Jedi general
“Word has reached me,” Palpatine was saying, “that a group of clone troopers on Murkhana may have deliberately refused to comply with Order Sixty-Six.”
Vader tightened his hold on the lightsaber. “I had not heard, Master.”
He knew that Order Sixty-Six had not been hardwired into the clones by the Kaminoans who had grown them. Rather, the troopers-the commanders, especially-had been programmed to demonstrate unfailing loyalty to the Supreme Chancellor, in his role as Commander in Chief of the Grand Army of the Republic. And so when the Jedi had revealed their seditious plans, they had become a threat to Palpatine, and had been sentenced to death.
On myriad worlds Order 66 had been executed without misfortune-on Mygeeto, Saleucami, Felucia, and many others. Taken by surprise, thousands of Jedi had been assassinated by troopers who had for three years answered almost exclusively to them. A few Jedi were known to have escaped death by dint of superior skill or accident. But on Murkhana, apparently unique events had played out; events that were potentially more dangerous to the Empire than the few Jedi who had survived.
“What was the cause of the troopers’ insubordination, Master?” Vader asked.
“Contagion.” Palpatine sneered. “Contagion brought about by fighting alongside the Jedi for so many years. Clone or otherwise, there is only so much a being can be programmed to do. Sooner or later even a lowly trooper will become the sum of his experiences.”
It's not possible. Any healthy clone who received Order 66 would be compelled to kill nearby Jedi. This is revealed in the first arc of final season of The Clone Wars. A clone mysteriously murders the Jedi leading their platoon. During the investigation into why this occurred, it's revealed that all clones have a brain implant that reacts to Order 66. When triggered, the clone then kills nearby Jedi.
So any healthy clone (i.e. has a functional brain implant) who receives Order 66 would follow the order.
We know that Captain Rex, Commander Wolffe, and Gregor did not follow Order 66 or at least did not join the Empire. This is the only canon material we know of, but outside of canon...Captain Maze, Ordo, Delta Squad, Omega Squad, Ion Team, 3 ARC troopers with Shaak Ti, HOB-19, and a few others did not follow Order 66.
Source: Clone Wars There was a single clone, Fives, that disabled his implanted chip. Unfortunately it was believed that the chip made the clones loyal (this is shortly before Order 66) and that Fives chip had malfunctioned in a way that made him crazy. He never managed to prove that he was getting framed. In the end he died from a shot. He did manage to uncover it all and even told Anakin and Rex it all (Rex is another clone). This was the story of the first 4 episodes of season 6 as release on Netflix. Another post here mentions Rex amongst other clones that didn't fall to order 66. He could be right, as Rex was listening to Fives last words. However some of these sources are probably part of the expanded universe, so everything could happen. It is possible, even likely, some of the troopers present at Fives death, including Rex, managed to take action before Order 66. But it is during the same season Anakin goes dark side, so I would have to assume they do it without him knowing.
Depends on what you consider canon. Prior to the ending of the Clone Wars TV series there were numerous examples of Republic soldiers not following Order 66, one of the main examples being the Republic Commando book series. This is not the first case of that show messing with pre-established canon, unfortunately however, with the sale of Star Wars to Disney, it is one of the few sources now officially recognized.
HOB-147, a clone pilot, disobeyed Order 66.
some clones refused to follow order 66 such as omega squad and instead help the jedi's escape and the whole thing in star wars the clones wars about the clones have organic chips is true but the clones completely obeying all order is bull coz there are many account of clones not executing order 66 and refusing to do it or some thought it was a joke