The old rule used to be to never use it. And many people followed the rule, whether or not it made sense.
But with the advent of e-mail and computers more people are writing, the old rule is no longer as dictatorial, and variations are permitted.
Realistically, the more formal your writing needs to be, the less you should use "but" or "and" to start a sentence. There's usually a clearer way to get your point across. I work in technical writing and shy away from it on the job as a matter of course.
But in more creative writing and/or informal writing (such as journaling or letter writing or posting things on Yahoo Answers!), I think it's perfectly acceptable to start a sentence with "but" or "and."
Usually it is used for give "flavor" to the text, to give it some life and personality. And it forces people to pause or breathe where you'd like them to, when they read your text "mentally" in their mind. You're not just relaying information, you're trying to make your reader feel certain things, and such constructions are one tool to do that.
But I suppose it's really up to you.



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