I've seen this done more and more recently, but I always thought it was wrong to start a sentence with 'but'. Is it like ending a clause with a preposition - it's not WRONG but just frowned upon?
In most cases, it is grammatically incorrect and you can almost always rewrite a sentence to not start with that word. However, certain times when the author wants to make a statement, they make it stand out, by separating a compound sentence. Also, when writing dialog, almost anything can go. Any English major will tell you that speech has almost no grammatical rules so therefore, dialog is loose as well.
If you see a sentence as an idea contained all between the first word and the full stop, you can see the contradiction easily of starting with "and" and "but"... Most of the time you'd write it, it could just be misinterpreting a pause as a full stop because it feels more dramatic that way. Of course, I've mostly encountered sentences with a "but" in the middle of them in academic writing, so it feels very much like a way of extending a sentence to me. I've noticed in fiction when editing down you can take out so many of the "but"s and "however"s etc etc and the thing still makes sense. Only in cases where you really want to emphasise the contradiction would you really have to use it. Words like that do become sort of placeholders and ways of naturally padding out a sentence to aid the flow which don't always have to be in there. A contradiction stated clearly will still look like a contradiction without a "but" before it, making it really obvious for the reader. (but yeah, obviously you can do it all the time in speech )
If you are doing formal writing for school, business, a trade magazine, etc., i would highly advise against doing so. However, as time has progressed in popular fiction, it seems more and more acceptable to start a sentence with a coordinating conjunction. And personally I'm fine with that.
Of course, you can have a great emotional effect if you pull it off right by starting a whole paragraph worth of sentences with "But", if you really know what you're doing. Wouldn't be sure if I could do it myself, but someone could.
In fiction it gets used all the time. The intent usually (I said usually) is to add impact to a statement that goes contrary to the expected. Timothy truly believed that Mary would call the next day. But she didn't. He became despondent. Remember that fiction is a more flexible creature than formal writing. This is not an excuse, though, to not know your grammar and syntax.
Agreed with Wrey -- if you're a good writer and you know all about polysyndeton and asyndeton, and can pull it off to get the right tone and you really know what you're doing...go for it. If you're not as experienced, don't. You'll look like you don't know your grammar.
Last time I saw it was on a BBC news article - that's what reminded me to post the question. You know, I never really thought about that before. Thanks Melzaar. EDIT: Just checked my ms and found I've used but 67 times in 6300 words. More than 1%!
It's not considered good style in academic writing, and it can be a bit choppy to have sentences starting with 'but', 'or', 'and' etc. However, this can actually be a useful side affect, I mean one you can deliberately use, in writing fiction. Wrey's example is nice. You can see how it makes the writing edgy--like Timothy feels! Just don't overdo it, as has been noted above.