I was interested to hear about spacing after periods in class today, so I decided to look even further. I was disturbed to hear that one space after periods was expected in the Internet. Luckily, I have a way out.
According to APA style (6th edition), one should "Use two spaces after periods instead of one. More space in between sentences allows for easier reading and comprehension".
However, MLA says differently. One should "Leave only one space after periods or other punctuation marks (unless otherwise instructed by your instructor)".
And Chicago also agrees, saying "that there is no reason for two spaces after a period in published work". Chicago does go on to say that some people prefer two spaces, however.
I think that it is a matter of personal preference, or which style guide we are using. So, as someone who is writing exclusively in APA (thank you, Faculty of Education), I will stick to two spaces. Besides, I won't have to re-learn anything!