In general, censorship is not supported by the First Amendment to the US Constitution nor by the ALA Bill of Rights in Libraries in the US. Of course, prison libraries are under very different conditions. According to Geary, Mike. "Trends in Prison Library Service." Bookmobile and Outreach Services 6, (2003) "It is important to keep in mind that prison librarians are part of the organization that locks up the prisoners. They are professionals who serve the institution as well as the inmates. Basic beliefs in intellectual freedom, censorship, and public service may all be compromised."
The Federal Bureau of Prisons (BOP) regulations state that publications can only be rejected if they are found to be "detrimental to the security, good order, or discipline of the institution or if it might facilitate criminal activity." That description is generally understood to include content such as explanations on how to make explosives, martial arts training manuals and books containing maps of the prison and its surrounding area. Each prison governor has the discretion to ban access to any reading material if he or she considers that the content presents a threat to good order or discipline, or that possession of the material is likely to have an adverse effect on the prisoner’s physical or mental condition. More at Cornell University Law School online.
In addition, books can be harder to access inside for numerous reasons. Also, some restrictions are also placed on buying and where to buy items as well as other factors surrounding vending/acquisitions. Many prisons use the IEP (earned privileges) or similar schemes as well. Most prisons also prohibit obscene or explicit materials. However, it is fairly difficult to find express polices around this topic due to the controversy surrounding this topic. You may of course contact each DOC separately to find out more about what they do in each state or jurisdiction that you are interested in. Banned lists are not always easily accessible or publicly available but may be available to you upon further request. You may also share them with us later if you do find any more comprehensive lists yourself. The ACLU has filed motions in a US district courts that argue an existing policy at places like the Berkeley County Detention Center in Moncks Corner, S.C., is unconstitutional. The policy currently bans all reading material — save the Bible — from inmates. Read more:
Some states do supposedly maintain lists of banned items. The Texas Department of Criminal Justice is unique in that it supposedly maintains a statewide database of banned books. "The Texas Department of Criminal Justice (TDCJ) arbitrarily censors books and magazines sent to Texas prisoners. Though cultivating literacy has obvious rehabilitative benefits, TDCJ prevents prisoners from reading many books, including works by award-winning authors, literary classics, and books about civil rights and prison conditions. Many feel that it is in violation of prisoners’ First Amendment rights that TDCJ prohibits the of reading important books."
Banned Books in the Texas Prison System (2011)
The Virginia Department of Corrections (DOC) also allegedly maintained a list of books partially named on this site.
It is important to note that in 2013, a pair of civil rights organizations sued the Virginia Department of Corrections after the groups’ inmate legal guide to challenging prison mistreatment reportedly was banned. The suit, which was filed in Charlottesville’s federal court by the National Lawyers Guild and Center for Constitutional Rights, said that the “Jailhouse Lawyer’s Handbook” was banned without the required notice to the publisher. The groups also accused the department officials of violating their First Amendment rights.
In any case, there certainly isn't any one single nationwide list of books or magazines banned from prisons, but here is a list of resources which may help you explore this topic further: