A Study Bible of your preferred translation
Concordance (references Bible verses/words/phrases)
Catechism or compilation of sermons of your choice. If Jewish, a copy of the Talmud.
If Christian, copies of Nicene and Apostle's Creed
Declaration of Independence
U.S. Constitution with Amendments
Shakespeare's Hamlet, Macbeth, Henry IV, Romeo and Juliet, Much Ado About Nothing
George Bernard Shaw's Major Barbara and Pygmalion
Two arithmetic books focusing on story problems and using "units" to guide problem solving
One textbook each focusing on grammar and sentence construction
College level dictionary
Spanish/English translation guide
Peter's or Bartlett's Quotations
Handwriting guide (D'Nealian or Palmer)
National Electric Code. Does not need to be most recent issue
Principles of Chemistry textbook
Climate-appropriate book(s) on gardening
Basic book on human nutrition with emphasis on foods that are rich in essential vitamins and minerals
Bubel's guide to Root Cellaring (low tech, low energy)
Ball's Blue Book to Preserving (canning), any issue
Books on plumbing, "farm" carpentry, heat-treatment of carbon steels, trapping, tanning hides, etc. The list is almost endless.
Merck's Handbook of Veterinary Medicine
A book on general animal husbandry and animal breeding (including issues with inbreeding depression).
Combat Skills of the Soldier (FM-75)
Field Manual of Preventative Medicine: Preventive Medicine for Ground Forces
Advanced First Aid Manual (emphasis on exposure, burns, bleeding and poisoning)
Basic book on physical fitness with "bogeys" for sit-ups, pushups, pullups and three-mile run by age-group and gender.
Biographies of notable people: Thomas Jefferson, Louis Pasteur, Robert Koch, Joseph Lister, Daniel Boone and others
Fiction by Mark Twain
Blackstone's Commentary on Law
Various Boy Scout merit badge books
Set of Encyclopedias in the 1935-to-1965 vintage.
Please feel free to add to the list. I am sure I missed wide swaths of literature. I tried to stick with categories rather than list specific books.
I am moving comments to the main body since not everybody reads the comments
Nominated by Markshere2: Firefox collection Backwoods home collection
Nominated by Lucky_P: Books on identifying, using, and eating wild, native plants and mushrooms. Any of Sam Thayer's books, like 'Forager's Harvest', etc. would be worth having on hand if you're in the eastern or midwestern US. I've not yet hit on the best mushroom ID guide with emphasis on edible species.
LJW wrote: If you have a Kindle - get the Complete Harvard Collection! It is $1.99 and has a lifetime of reading.
I want to add: The Prince by Niccolò Machiavelli
A college freshman level primer on Macro Economics and another on Micro Economics. Incidentally, older editions of college textbooks are often screaming bargains and they are usually exceptionally well bound.
Nominated by tweell: Where There is no Doctor, Where There is no Dentist. Decline and Fall of the Roman Empire, Gibbons. Democracy in America, Tocqueville.
Nominated by Old NFO: The Iliad and the Odyssey
Nominated by Roger: Plutarch Essays and Lives I & II and Marcus Aurelius - Meditations
A set of the "Dick and Jane" reading books and a set of McGuffy's Readers.
Improvised Medicine by Kenneth Iserson. Armageddon Medicine by Cynthia Koelker. Prescription for Herbal Healing by Phyllis A Balch. A relatively current copy of the Physician's Desk Reference.
Volumes 1-4 of The Bowyer's Bible
Pocket Ref and Desk Ref by Thomas L Glover
Stocking up, and old Rodale Press book. Get the latest you can find.
A 1910 copy of the Encyclopedia Britannica. Mine's on CD, but I'd love a real copy.
Gardening When It Counts by Steve Soloman.
A copy of the Chemical Rubber Handbook.
A complete set of the Sherlock Holmes stories by Sir Arthur Conan Doyle.
A complete set of the works of Robert A Heinlein.
The Makeshift Workshop Skills series by James Ballou.
The Leatherworking Handbook by Valarie Michael.
ARRL handbooks, especially the ones on wire antennas. The RSGB also has good books on the same subjects.
Early 1900s copies of the Boy Scouts and Girl Scouts handbooks.