What enchantments can books have?

Based on enchanting 11 books in vanilla Minecraft all at level 30 in survival mode

1. Books appear to be able to receive all enchantments that can be used on other items.
2. Books only ever receive a single enchantment.

3. Don't know the answer to this, but here are the 11 enchantments I got:

   • Protection III
   • Sharpness III x 2
   • Unbreaking III x 3
   • Fire Protection III
   • Blast Protection IV
   • Efficiency III
   • Punch I
   • Power IV

What is an enchanted book?

According to the Minecraft Wiki, an enchanted book is an item which allows players to add enchantments to weapons, tools, or armor by combining the enchantment book with one of said items on an anvil.

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Can they receive any enchantment?

Testing in creative and survival mode shows that books can receive any enchantment that a normal weapon/armor/tool/other can receive. An easy way to check is to go into creative mode and use the new search function to search for the term book. This will show you what all the enchanted books are.

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Can they receive more than one enchantment?

According to the wiki, books may only have one enchantment. This can be tested by giving yourself a bunch of books and enchanting them, then throwing them into lava or whatever you wish to do with them.

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Since enchantments have different chances of occurring for different tools, materials, and at different levels, how are those probabilities different for books?

This would be different for books since books are not diamond swords. However, this would have that many variables because unlike a sword, books can only be made from paper. Swords can be made from diamonds, iron, and other materials. You would have to test this to truly know, but if John tells us how many levels he invested into his enchanted books, we might be able to know. Right now, though, it appears that the enchantment gives you the highest level (ex. Protection IV, Sharpness IV, etc.)

A lot more information has become available since the question was asked. I think the most detailed answer is available on the wiki as an excel datasheet on the enchantment mechanics page. A nicer summary is available on the Book page at minecraft-enchantments.net, although their level 30 odds seem to sum to higher than 100%! Another resource that's useful when looking for a specific enchantment, is the enchantment calculator.

A quick summary is that books enchanted at level 1 can get one of 5 enchantments:

• Power I (~25%)
• Sharpness I (~24%)
• Protection I (~24%)
• Efficiency I (~22%)
• Aqua Affinity I (~5%)

While books at level 30 can get any one of 22 enchantments* and each also at a variety of different levels (always at least the highest two levels). The odds of any type of enchantment (at any level) is never higher than 10% and never lower than 1.5%. The most common four are still the same as at level 1, although they only appear between 5% to 10% of the time. Rarest of all are Infinity, Silk Touch and Thorns.

*The 22 enchantments are: Aqua Affinity, Bane of Arthropods, Blast Protection, Efficiency, Feather Falling, Fire Aspect, Fire Protection, Flame, Fortune, Infinity, Knockback, Looting, Power, Projectile Protection, Protection, Punch, Respiration, Sharpness, Silk Touch, Smite, Thorns and Unbreaking.

Actually, I have received two enchantments on a single book, though it appears to be extremely rare. However, they may be any enchantments, and may no be similar in any way.

MINE: Level enchanted-17, Enchantment 1-Fire Protection II, Enchantment 2-Power II,

No useful at all, as a bow is worthless with protection and armor useless with power. basically a piece of worthless junk, but never the less, two enchantments in one book.

BTW - two books can be combined in an anvil and get more than one enchantment that way, and obviously with the /enchant command.

Actually you cannot get two enchantments on one book but to get sharpness and protection which are the most useful in combat just enchant a lot of books with level one then combine them in an anvil to get a better level.

Note:you must use the same kind of book to level it up ex: 1 + 1 = 2 ex: 1 + 2 = nothing ex: 2 + 2 + 3 And on and on

An enchanted book, according to the wiki, is

An enchanted book is an item which allows players to add enchantments to certain items using an anvil.

Going from creative to survival can assist you to view all the enchantment books, or enchant, whatever you please, all 22 enchantments¹. Also according to the wiki, multiple enchantments can be placed per book. You can also test this by either using the /enchant command, or manually enchanting the books.

^{1: All the 22 enchantments include- Aqua Affinity, Bane of Arthropods, Blast Protection, Efficiency, Feather Falling, Fire Aspect, Fire Protection, Flame, Fortune, Infinity, Knockback, Looting, Power, Projectile Protection, Protection, Punch, Respiration, Sharpness, Silk Touch, Smite, Thorns and Unbreaking. These can also be upgraded to II, III,IV.. etc.}