Since computers, basically.
People were taught to put two spaces between sentences when using typewriters because typewriter characters are monospaced (i.e., all of the characters are the same width), which generally makes the text look really uneven. Two spaces were necessary so you could actually see the end of a sentence.
This isn't a problem when typing on computers because the characters are proportional (except when using a typeface like Courier, which is intentionally monospaced). Two spaces between sentences is overkill.
Wrong Mr. BertramCooper, it's because typographically there should be more space after a sentence-ending period than interword space or after an abbreviation-ending period, such as Mr. Because unfortunately typography on the Web and in Word sucks.
(you can't see because html collapses the spaces)
^ tl;dr Opus was right.
Edit: identical space across the board is called "french spacing".