It’s not completely one or the other, as many say.
It depends entirely on whether the font is fixed width or proportional.
Proportional fonts look like this. Only one space is ever needed because the words group better and thus it is not difficult to discern the end of any sentence that has only one space. ABCDEFGHIJKLMNOPQRSTU
Contrary to the general layman’s belief, there are still many good uses for fixed width fonts. For instance when setting apart text as “written with a typewriter” in a novel. Or when you’re commenting in software code. Some screenwriters still use fixed width fonts, and those that do will need to use two spaces between sentences.
Whenever you’re using a fixed width font, and speaking semantically, use double spaces between sentences to improve readability. Old typewriters required it, but unless you are enjoying clacking away on a 1930s typewriter, there is no reason to do so.
When using a proportional font – regardless of your personal preferences, use only a single space. In fact, a basic rule of word processing used to be that there is never a reason for two whitespace characters in a row. For instance a space followed by a tab, a tab followed by a paragraph break, a tab followed by another tab, etc. (I’m not sure it really matters to be that particular, unless you want to make global search and replace changes to the styles applied to many word processing documents at once. )
but the fact remains that most of us don’t need to worry about this, and you can easily read words with proper proportion applied and can tell where sentences end without the extra space. It is just as annoying to have too large a space between sentences as it once used to be to not have enough.