Feel free to look up the related history, but please note that no major manual of writing style or formatting indicates the need for extra space anywhere.

Specifically, use only one space at a time anywhere in documents created in word processing software (or simple text editors, for that matter). Don’t put two or more spaces together, adjacent. Use one between words, sentences, etc. The same goes for the tab. Never use more than one at a time. Move the tab stop to where it needs to be. Only one tab for any amount of space, and then when you edit, things don’t suddenly go wacky.

One tab, one space, never more in the same place.

If you look up the history, you will be hard pressed to see it ever used except in typing classes, where the teachers wanted the extra white space for markup. There was a time when lots of space was used, and it was highly variable. It seems it had to do with charge per page, more than anything else. Otherwise, publishing, especially news papers, always tried to minimize paper usage by minimizing white space usage. Again, you will be hard pressed to find any printed material that uses extra space between sentences, etc. Accordingly, arguments regarding readability don’t hold water. There isn’t any of it anywhere, so how can it be easier to read?

http://www.chicagomanualofstyle.org/qanda/data/faq/topics/OneSpaceorTwo.html

http://www.gpo.gov/fdsys/pkg/GPO-STYLEMANUAL-2008/html/GPO-STYLEMANUAL-2008-4.htm

2.49. A single justified word space will be used between sentences.
This applies to all types of composition.

So, with the respected Chicago Manual of Style and the US Government Printing Office Style Manual telling you specifically to not use two spaces, please don’t. It really causes problems in computer documents. Formatting nightmares ensue. (Of course, MS Word can cause plenty of formatting nightmares, so try not to add to them.)