There are some exceptions to the general rule to use only one space following a period at the end of a sentence. If you are writing a plain-text document that is likely to be viewed with a fixed-width font like Courier, it is often a good idea to insert two spaces after a period. “Plain text” includes no bold, no font choices, no font sizes, etc., just letters, numbers, punctuation, and manually-entered whitespace like newlines and indents created with space characters.

Here are some examples of documents that are created using fixed-width fonts (in some cases they can be viewed with variable-width fonts, but in other cases they are viewed with fixed-width fonts):

1. Almost all computer programming is still done with fixed-width fonts because the vertical alignment of things tells a lot about their logic; although there aren’t real sentences in the programs themselves, they tend to be full of comment blocks explaining (with English text) what is going on, and those typically still use two spaces after periods. HTML tags are included in this type of document.
2. Another place where people write in “plain text” and often view with a fixed-width font is in so-called README files that you find online explaining what is in a folder (for example), or at the top of a CD-ROM explaining the contents.
3. Basic email is sometimes written in “plain text,” for example, from a Blackberry, and that will sometimes be rendered by email programs (the recipient’s viewer) in a fixed-width font.
4. For academic dissertations, some universities still follow an APA Style recommendation to include two spaces after a period in “draft” manuscripts. There seems to be a good deal of confusion about this point, and most editors recommend checking with a specific university’s style guidelines.

I would like to acknowledge the assistance of my “software genius” brother Alan Rooks for explaining the first three points above to me. More details are available if required.