Well, yeah, that’s the question - one of my students mentioned that the powers that be have decided it is indeed now acceptable to end a sentence in a preposition, so it would be grammatically correct to say ‘Who are you talking to?’ instead of having to say “To whom are you talking?” Is this just a myth?
This is the sort of bloody nonsense up with which I will not put.
Here is a link prepositions I am not sure it is authoritative, but it may help.
You should never end a sentence with but.
Are you sure you are not referring to the antiquated rule of never BEGINING a sentence with BUT? I cannot imagine any English speaker ending a sentence with BUT.
But starting a sentence with it is even worse.
But you just did it. 
(do not missunderstand, I got it. BUT I was just playing along.)
I’m not sure which version of English you’re asking about, but I can offer an opinion on the matter. Of course, this is “American English”.
First, I still don’t know why we just don’t call it American, as opposed to English. But I digress.
The American form of English is vastly more expressive and shifting compared to the Queen’s English. Hell, the US has almost 300 million people, and with different dialects, sometimes we miss a word or two between ourselves.
The point is, what becomes common use, becomes standard use. By default, it becomes the newest rule. Basically, if the listener understands the message in proper context, by default it’s a proper sentence. (Yes, yes, this pisses off English teachers, but I’ve heard educators say “aks” instead of “ask”).
Linguistics aside, I think it’s funny how the world looks down on a perceived lack of American culture, then hits us for stylizing our language to something unique.
Just a thought. I return you to your regularly scheduled thread. 
<that Bork guy in *Beavis and Butthead> “Say, chief, isn’t that the guy in whose camper off they were whacking?” </Bork>
Strictly speaking, one should be using “but” as a conjunction and not end the previous sentence. If one speaker is speaking both sides of a conjunction (or disjunction) they should use an entire sentence. Beginning a sentence with “but” is best used as a rejoinder, in which case one is implicitly finishing the previous speaker’s (implicitly unfinished) sentence.
This is acceptable West of Scotland dialect use, but.
It means the same as putting it at the beginning.
Every form of speech is vastly more shifting than the ‘Queen’s English’. The whole point of the ‘Queen’s English’ is that it doesn’t shift, it’s a prescriptive standard and very, very few people speak it, including the Queen. (She gets close, but as has been noted recently her speech patterns have changed in the last twenty years.)
So the American form is really no different from any other usual, everyday, dialect of English and the speakers of it aren’t doing anything smarter than anyone else.
I can’t agree with your ‘more expressive’ analysis either. All languages and dialects are pretty much at an equal, and that includes speakers of “the Queen’s English”. The only difference is in the skill of the speaker and the understanding of the listener.
Quoting the Chicago Manual of Style:
Amusingly, the index entry was “Prepositions, ending sentences with.”
I agree that there was nothing ever grammatically incorrect about ending sentences with prepositions.
English is not the first language of Peru, but the people of Chile are certainly American. At least, that’s how I picture it - has “American” gotten synonymous with “North American” over the years?
Yuppers. Longs u kin undrstnd wut im sayn, dont matter how I rites it. I makes the rool. Soons i wrights it it becomes a propr sentce by fault.
Y everbuddy thinx us Amerkns is ignernt i jist duznt git. We just be stylizin are langauege to sumpin uneek, definin our Amercn culcher. Spellin however we feel like & usein words however we feel like is wut makes us truely Amercan. And also to, only N. Ameirca is real Amaircka, cuz everbuddy comonly callz us it.
Grammer? WE dont need no stinkn grammr! Ifn u cn rd ths, it provs my pt.
Clarity should take precedence over grammar, always!
“Thou shalt not end a sentence with a preposition.” is one of those monumentally stupid prescriptive grammarian rules imposed by monumentally stupid prescriptive grammarians in an attempt to “Latinize” English. It’s as boneheaded as “Thou shalt not split an infinitive.” English, being a Germanic language, can easily end a sentence with a preposition. Indeed, there are times when a preposition is the best thing to end a sentence with.
See also: Seperable prefixes of German verbs.
The little boy who was sick in bed said to his Mom, “What did you bring that book I don’t want to be read to out of up for?”
American Tourist in London: Excuse me. Can you tell me where Buckingham Palace is at?
Londoner: I shall tell you, my dear fellow, when you learn not to end a sentence with a preposition!
American Tourist: Okay. Can you tell me where Buckingham Palace is at, ASSHOLE?
Yes. The spoiled brat complained because it was a book about Australia, which he didn’t like. His mother attempted some feeble excuse, and after a few moments he sighed: “Will you get your explanation of what you brought that book I don’t want to be read to out of about Down Under up for over with?”