This is how I was taught, and rightly so. It looks better. It enhances readability, especially when the font doesn't have capital letters of full height or the period seems rather tiny, or both. And it has historical backing in that printers of old would use an enhanced space after the period, which was translated in typewriting as two spaces. There is no reason to change it . . . it makes computer searching for sentences much easier, too, because otherwise you can't tell the difference between the end of a sentence and Dr. McCoy.
Now, however, there are forces bound and determined to destroy this readability and utility and force a single space upon the world, making everything into run-on-sentence gobbledygook on the grounds that some typographers think whitespace "looks bad". They are small in number and mind, but have some power and seek to exercise it on us all, and I've seen quite a few vicious attacks on unsuspecting double-spacers . . . assaults on the innocent for no good reason, as double-spacing hurts no one.
So I say up yours, commie statist bastards! I'm reading to get information, not worry about your entirely-too-nuanced (read: stupid) aesthetic opinion of white space on a page. You want no white space? Stop using the spacebar entirely, and see how far that gets you.
I kid you not, this is literally the reason why ST-v-SW.Net isn't going to go the same way I have gone with NoLettersHome, which is using MediaWiki. MediaWiki's makers enforce a single space in their wiki parser, so that even if you put two the second gets cut out. Were it not for certain needs MediaWiki and plugins can fulfill, I would run away from such Apple-esque thinking.
Next up . . . 2S-v-1S.Net . . . the final apocalyptic battle of good versus evil.
Remember, when you use only one space after a period, the terrorists win.