It turns out that just about everyone who reflexively types two spaces after a period either learned to type on a typewriter or was taught by someone who learned that way. Spacing on typewriters was different than most of today's electronic fonts; each character used to get the same amount of space, making the end of a sentence difficult to distinguish visually, but most fonts today are proportional, rendering that extra space after a period (or after a question mark, or after an exclamation point, or on either side of an em dash) unnecessary.
Many people who learned the two-space rule don't (or can't) let go of it easily, and for the most part that's okay. There are whole industries that still adhere to it, and there are also those who insist that the extra space is still necessary for readability (although apparently not as many as those who insist that it detracts from readability). However, I am for the most part a supporter of "changing with the times," and I do want people to know that in this modern high-tech society such habits can be viewed negatively. Particularly if you're submitting, say, job applications, adherence to this outdated rule can be seen as indicating a resistance to change or, unfortunately, used as a tool for age discrimination. File this one under "good to know"!