Answer:
"All that is necessary for the triumph of evil is that good men do nothing." (Edmund Burke)
Numerous searches by numerous people have failed to find this exact quotation in any of Burke's writings,and it is now thought to be a 20th Cen. paraphrase.
Here is an Edmund Burke quote that I believe fits nicely into the above 'paraphrase?':
"It is not enough in a situation of trust in the commonwealth, that a man means well to his country; it is not enough that in his single person he never did an evil act, but always voted according to his conscience, and even harangued against every design which he apprehended to be prejudicial to the interests of his country. This innoxious and ineffectual character, that seems formed upon a plan of apology and disculpation, falls miserably short of the mark of public duty. That duty demands and requires that what is right should not only be made known, but made prevalent; that what is evil should not only be detected, but defeated. When the public man omits to put himself in a situation of doing his duty with effect it is an omission that frustrates the purposes of his trust almost as much as if he had formally betrayed it. It is surely no very rational account of a man's life, that he has always acted right but has taken special care to act in such a manner that his endeavours could not possibly be productive of any consequence."
This is also a quote from the game Castlevania: Symphony of the Night by Alucard Draculas halfblood son. the exact quote being "Always remember, that the only thing necessary for evil to triumph is for good men to do nothing."