All that is necessary for the triumph of evil is that good men do nothing.
This is probably the most quoted statement attributed to Burke, and an extraordinary number of variants of it exist, but all without any definite original source. These very extensively used "quotations" may be based on a paraphrase of some of Burke's ideas, but he is not known to have ever declared them in such a manner in any of his writings. It may have been adapted from these lines of Burke's in his Thoughts on the Cause of Present Discontents (1770): "When bad men combine, the good must associate; else they will fall one by one, an unpitied sacrifice in a contemptible struggle."
Burke's alleged quote bears a striking resemblance to the narrated theme of Sergei Bondarchuk's Soviet film adaptation of Leo Tolstoy's book "War and Peace", in which the narrator declares "All that is necessary for evil to triumph is for good men to do nothing", although since the original is in Russian various translations to English are possible.
See some of the admirable research done on this matter at these two links: Burkequote & Burkequote2 — as the research at these links points out, there are many variants of this statement, probably because there is no clearly definitive original by Burke, some of them being:
All that is necessary for evil to triumph is for good men to do nothing
All that is necessary for the triumph of evil is for good men to do nothing
All that is necessary for evil to triumph is that good men do nothing
All that is necessary for evil to triumph is for a few good men to do nothing
All that is necessary for the triumph of evil is for a few good men to do nothing
All that is necessary for the triumph of evil is for some good men to do nothing
All that is necessary for evil to triumph is for all good men to do nothing
All that is necessary for evil to triumph is for enough good men to do nothing
All that is necessary for the triumph of evil is that enough good men do nothing
All that is essential for the triumph of evil is that good men do nothing
All that is needed for the triumph of evil is for good men to do nothing
All that is needed for the triumph of evil is that good men do nothing
All that is needed for evil to triumph is for good men to do nothing
All that is needed for evil to triumph is that good men do nothing
All that is needed for the triumph of evil is for enough good men to do nothing
All that is needed for the forces of evil to triumph is for enough good men to do nothing
All that is required for the triumph of evil is that good men do nothing
All that is required for the triumph of evil is for good men to do nothing
All that is required for evil to triumph is for good men to do nothing
All that is required for evil to triumph is that good men do nothing
The only thing necessary for the triumph of evil is for good men to do nothing
The only thing necessary for evil to triumph is for good men to do nothing
The only thing necessary for the triumph of evil is that good men do nothing
The only thing necessary for evil to triumph is for good men to do nothing
The only thing required for evil to triumph is for good men to do nothing
The only thing needed for evil to triumph is that good men do nothing
The only thing needed for the triumph of evil is for good men to do nothing
The only thing that is necessary for the triumph of evil is for good men to do nothing
The only thing that is necessary for the triumph of evil is that good men do nothing
All that it takes for evil to triumph is for good men to do nothing
All it takes for evil to triumph is for good men to do nothing
All that’s necessary for the triumph of evil is for good men to do nothing
All that’s needed for the forces of evil to triumph is for enough good men to do nothing
All that’s needed for the triumph of evil is for good men to do nothing
All that is necessary for evil to succeed is for good men to do nothing
For evil to prosper all it needs is for good people to do nothing
All that is necessary for the forces of evil to win in the world is for enough good men to do nothing
All that’s necessary for the forces of evil to win in the world is for enough good men to do nothing
All that is required for evil to triumph is for good [wo]men to do nothing
The only thing needed for evil to triumph is for enough good men [and women] to do nothing
The only thing required for evil to triumph is for good men (and women!) to do nothing
All that is necessary for evil to triumph is that good men (and women) do nothing
All that is necessary for the triumph of evil is that good men (and women) do nothing
For evil to triumph it is necessary only that good men [and women] do nothing
All that is necessary for evil to triumph is for good men and women to do nothing
All that it takes for the triumph of evil is that good men and women do nothing
The only thing necessary for the triumph of evil is for good men and women to do nothing
All it takes for evil to triumph is for good people to do nothing
All that is necessary for evil to triumph is for good people to do nothing
All that is necessary for the triumph of evil is that good people do nothing
All that needs to be done for evil to prevail is that good men do nothing
The only thing that has to happen in this world for evil to triumph is for good men to do nothing
All that is necessary for evil to triumph in the world is for enough good men and women to do nothing
Evil thrives when good men do nothing
For evil to triumph good men need do nothing
For evil to triumph good men have to do nothing
The best way for evil to triumph is for good men to do nothing
The surest way to assure the triumph of evil is for good men to do nothing
Evil will triumph so long as good men do nothing
It is necessary only for good men to say nothing for evil to triumph
It is necessary only for the good man to do nothing for evil to triumph
For evil to triumph it is necessary for good men to do nothing
For evil to triumph it is sufficient for good men to do nothing
All it takes for evil to triumph is for good men to stand by and do nothing
All that is necessary for the forces of evil to triumph is for good men to do nothing
All that is required for evil to triumph over good is for good men to do nothing
Evil can triumph only if good men do nothing
The only thing evil men need to triumph is for good men to do nothing
The only thing for the triumph of evil is for good men to do nothing
The only thing necessary for the triumph of evil is for enough good men to do nothing
The only thing necessary for the triumph of evil is that good men stand by and do nothing
The only thing necessary for the triumph of evil was for good men to do nothing
The only way for evil to triumph is for good men to do nothing
Evil prevails when good men do nothing
