How many bits is a "word"?

In addition to the other answers, a further example of the variability of word size (from one system to the next) is in the paper Smashing The Stack For Fun And Profit by Aleph One:

We must remember that memory can only be addressed in multiples of the word size. A word in our case is 4 bytes, or 32 bits. So our 5 byte buffer is really going to take 8 bytes (2 words) of memory, and our 10 byte buffer is going to take 12 bytes (3 words) of memory.

This is from the book Hackers: Heroes of the Computer Revolution by Steven Levy.

.. the memory had been reduced to 4096 "words" of eighteen bits each. (A "bit" is a binary digit, either a 1 or 0. A series of binary numbers is called a "word").

As the other answers suggest, a "word" does not seem to have a fixed length.

I'm not familiar with either of these books, but the second is closer to current reality. The first may be discussing a specific processor.

Processors have been made with quite a variety of word sizes, not always a multiple of 8.

The 8086 and 8087 processors used 16 bit words, and it's likely this is the machine the first author was writing about.

More recent processors commonly use 32 or 64 bit words.

In the 50's and 60's there were machines with words sizes that seem quite strange to us now, such as 4, 9 and 36. Since about the 70's word size has commonly been a power of 2 and a multiple of 8.

The second quote is correct, the size of a word varies from computer to computer. The ARM NEON architecture is an example of an architecture with 32-bit words, where 64-bit quantities are referred to as "doublewords" and 128-bit quantities are referred to as "quadwords":

A NEON operand can be a vector or a scalar. A NEON vector can be a 64-bit doubleword vector or a 128-bit quadword vector.

Normally speaking, 16-bit words are only found on 16-bit systems, like the Amiga 500.