Typographically speaking, typing two spaces after a period ending a sentence is the wrong thing to do.
Extra space after a sentence was popular around the 19th Century, but these days it is no longer in fashion. By default LaTeX still adds the extra space, and you can turn it off with \frenchspacing. Don’t forget TeX’s typesetting was inspired by early 20th Century textbooks and you can understand why the extra space is the default.
But let’s get this clear: this extra space was used to help justify the lines of type without overly increasing the space between words inside the sentences themselves. That is to say: the extra space was not exactly two spaces wide. For some sentences it was more, sometimes less. (In some old books the extra space can be grotesquely large to my eyes.)
When typewriters came along, they needed all of the readability improvements they could get. Using a double space after the period works well to separate sentences that would otherwise run into each other visually. But proportional text doesn’t have the same problems.
Even if you wanted to add extra space after your sentences, it should be the job of the typesetting program to do this for you. Just like you shouldn’t hit Return twice in Word to separate paragraphs (if you know what you’re doing), you shouldn’t hit Space twice to separate sentences.
The only acceptable time I can concede that the double space is appropriate is for markup reasons. LaTeX does not support this, but a typesetting program that only added extra space in conjunction with the double space would be a little more elegant in cases where a period doesn’t end the sentence (e.g., after an abbreviation). I’m not a big fan of LaTeX’s syntax in this instance: cf.\@ previous, where the \@ suppresses the extra space that would normally be inserted. Luckily TeX is clever enough to assume that a period following an uppercase letter will generally not be ending a sentence, and suppresses the extra space automatically.
Phew.
Let’s just make life easy for ourselves and use \frenchspacing.