Wikimedia says: From around 1950, single sentence spacing became standard in books, magazines and newspapers. However some sources still state that additional spacing is correct or acceptable. The debate continues, notably on the World Wide Web—as many people use search engines to try to find what is correct. Many people prefer double sentence spacing for informal use because that was how they were taught to type. There is a debate on which convention is more readable, but the few recent direct studies conducted since 2002 have produced inconclusive results.
But let’s not just rely on WIkimedia. Let’s go to the pros. The Chicago Manual of Style and the AP Style Manual. The Chicago Manual of Style says:
The view at CMOS is that there is no reason for two spaces after a period in published work. Some people, however—my colleagues included—prefer it, relegating this preference to their personal correspondence and notes. I’ve noticed in old American books printed in the few decades before and after the turn of the last century (ca. 1870–1930 at least) that there seemed to be a trend in publishing to use extra space (sometimes quite a bit of it) after periods. And many people were taught to use that extra space in typing class (I was). But introducing two spaces after the period causes problems: (1) it is inefficient, requiring an extra keystroke for every sentence; (2) even if a program is set to automatically put an extra space after a period, such automation is never foolproof; (3) there is no proof that an extra space actually improves readability—as your comment suggests, it’s probably just a matter of familiarity (Who knows? perhaps it’s actually more efficient to read with less regard for sentences as individual units of thought—many centuries ago, for example in ancient Greece, there were no spaces even between words, and no punctuation); (4) two spaces are harder to control for than one in electronic documents (I find that the earmark of a document that imposes a two-space rule is a smattering of instances of both three spaces and one space after a period, and two spaces in the middle of sentences); and (5) two spaces can cause problems with line breaks in certain programs.
A guide comparing AP vs. Chicago Manual of Style (not that these two need to be compared — they are for completely different purposes, even though my juniors insist on fighting me on this):
A note about colons and spaces: Although I, too, was raised to use two spaces after periods, colons, exclamation points, and question marks by a typewriting teacher who was alive during the Great Depression, it is no longer correct to do so, especially in this age of beautifully typeset materials. The fastest way to clean all these extra spaces from your copy is to use Microsoft Word to “find” two spaces and “replace” them with one space, and then repeat until two spaces cannot be found.
What I know from my two years of studying for my MA in Design is this. Modern typography, and WSIWYG computers, take the “second” space into account. In other words, there is a little more space after a period anyway. This is the way that books are published, newspapers printed, and so forth. This wave began with the Mac and I believe is fully part of the PC system as well. That having been said, my youthful detractors, I will say that there are real and meaningful differences between the Chicago Manual of Style and the AP Stylebook. I own both, in their latest incarnations, for this reason. AP Stylebooks dictate style in newspapers and sometimes magazines (hence the name Associated PRESS). The Chicago Manual of Style reigns supreme over book publishing, and has also been adopted by many other publishers, including magazines. Who dictates style over the web? Well, that’s an unknown. They both do … and I don’t mind which as long as they’re actually used. Most web sites are completely devoid of styled content.