Why is 666 regarded as the devils number?
17And that no man might buy or sell, save he that had the mark, or the name of the beast, or the number of his name18Here is wisdom. Let him that hath understanding count the number of the beast: for it is the number of a man; and his number is Six hundred threescore and six. While, in context, it is not clear that 'the beast' is actually the devil himself, what is clear is that the beast is evil and that a willingness to accept the mark of the beast brings eternal damnation with the devil in hell.
The similarities are only subtle though, because, like the beast, the devil wants worship to be directed to him (either directly or through any other means - as long as it is not directed to the one true God) and the devil also has totalitarian spirit of domination, he loves to control and force people to do things and enslave them, rather than merely persuading, which is what the beast is also into in the account in Revelation.
It comes from Revelation 13:18 "Here is where wisdom comes in: Let the one that has intelligence calculate the number of the wild beast, for it is a man's number; and its number is six hundred and sixty-six." The wild beast represents either world government or the UN, I forget which. In the bible, the number 6 represents something imperfect or bad, so 666 is emphesizing that it is really imperfect or unholy.