Using "and" and "but" at the beginning of a sentence?

I think that it really depends on the case, as you said, but I've generally felt that we have moved away from being very strict about having "and" and "but" in the beginning of the sentence. I think now it's a general rule of thumb that can be broken at appropriate times. I actually like it if autors break the rule sometimes. Authors break rules all the time! :D