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In the past — or at least, when I was in elementary school — periods/full stops were followed by two spaces. Lately, it's become more and more common to see just one space. In the modern world, should we still use two spaces between sentences, or is just one okay? Does it depend on the situation? Or are both acceptable, with the choice simply coming down to personal preference?
Actually, I feel a few of the other answers here (and even the question) are a bit simplistic: there's more to this issue than is indicated by the latest editions of the Chicago Manual of Style or Bringhurst's The Elements of Typographic Style. In lieu of a very long answer, let me point to the (long) Wikipedia articles on exactly this issue: