Can a state legally censor books, movies, plays, etc. that it considers to be obscene?

Answer 1

yes, if they truly are obscene.
"Obscene" speech is NOT protected by the First Amendment, so it can be completely banned. (Many states have laws banning obscene speech or books or films, but such laws are rarely, if ever, enforced).

Obscene speech/books/movies must be (at a minimum, under the constution)
Whether the average person, applying contemporary community standards, would find that the work, taken as a whole, appeals to the prurient interest,
Whether the work depicts/describes, in a patently offensive way, sexual conduct or excretory functions specifically defined by applicable state law [the statutes are really funny, because they have to specifically define every possible sex or excretory act!],
Whether the work, taken as a whole, lacks serious literary, artistic, political, and scientific value.
Miller v. California
http://en.wikipedia.org/wiki/Miller_test

If these are met, the state can regulate them, or can ban them in their entirety. But you can see that's a pretty high standard, and will vary a lot from state to state (since it's about the 'contemporary community'). There may be some states where pretty much any porn would be protected. There may be others where pretty much any porn (without a serious scientific, artistic, or literary purpose) would be banned (note that the scientific, artistic, or literary purpose is not based upon the community, but upon an objective nationwide standard).

(Child porn, which most people would call obscene, actually has a different test not related to Miller)

Answer 2

BACK IN THE 70S,ALL LARRY FLINT PUBLICATIONS (HUSTLER,CLUB MAGAZINES) WERE BANED IN THE STATE OF GEORGIA. FOR A SHORT WHILE,ALL DISTRIBUTION AND SELL COULD GET YOU JAILED.IT TOOK A COURT ORDER IN THE GA SUPREME COURT TO OVER TURN THE BAN.BUT THERE ARE SOME CITIES AND TOWNS WHO CAN USE THERE POWERS TO BAN THEIR SELL IN THEIR COMMUNITIES ,SIMILAR TO THE GUN BANS IN SOME AREAS AND NOT IN OTHERS.

Answer 3

no it cant , but it also doesn't have to offer them in state run facilities like schools and public libraries