I always leave two spaces after a period because I think it looks better and neater to thus separate two periods.
As I understand it most it is completely optional and most of the people I know who do it, do it for aesthetic reasons.
HTH

...it's ok
1 or 2 spaces after a period, although not necessary.

If you look at the (European) English Style Guide, as below, you will see there is only one space after the colon. http://europa.eu.int/comm/translation/writing/style_guides/e...

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Note added at 20 mins (2004-11-24 16:54:22 GMT)
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colon as well....

Good [European] typography would deprecate 2 spaces after a period / full-stop.

As other answerers have correctly pointed out, it is a hangover from a convention that was adopted when typewriters came in, to make for added clarity (because with traditional typography or handwriting, such spaces might naturally have been made SLIGHTLY wider than the others, whereas with the fixed spacing on typewriters it had to be either 1 or 2, nothing in between!)

In my view, modern technology now enables us to drop this ugly habit and return to at least some of the dignity of 'proper' typography, without any sacrifice of legibility.

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Note added at 17 hrs 29 mins (2004-11-25 10:02:38 GMT)
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Kathy, in her peer comment to Paula\'s suggestion above, makes a very important point! The double space can have all sorts of ramificiations, both in the publishing world, and even in simple wor-processing; double spaces scerw up all sorts of things, and can make \'search-and-replacing\' a nightmare.

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Note added at 22 hrs 5 mins (2004-11-25 14:38:53 GMT)
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In reply to Aubonmot\'s amended peer comment:
Oh yes, indeed, full justification almost ALWAYS seems ugly to me, at least as performed automatically by most w/p / DTP software. I have fond memories of the olden days, and the time I would spend lovingly justifying a page of text set in metal type, using the 4 standard sizes of space available --- not to mention all the cheats and \'getarounds\'! So tactile, typography to me will always be a very concrete art... Ah me, those were the days... not of wine and roses, but of linseed oil and lead-poisoning. :-)