The post metadata include publication date; in some themes (list here) they include publication time as well (next to the date). Date and time format are set in Settings > General.
Before the major changes brought about by the implementation of wp 2.7, you could get rid of the time stamp by selecting “Custom” in the settings and typing a space in the box, or the html for a space. Neither of the two works now: so, if the theme you’re using normally displays the time stamp, the only way to get rid of it is type something that will show up next to the date; for instance your nick or your initial (if the metadata don’t include post author – see here), or your city, or a combination of punctuation marks as a decorative element.
You can also paste the html for various symbols (see lists in this or other similar webpages); for example:
☤ for ☤
☉ for ☉
☀ for ☀
☆ for ☆
♬ for ♬
But watch out: some symbols may not show up correctly, or not show up at all, in Explorer. For more on this, see here.
wordpress tips 
Talking about destroyplorer, spammers are on to the issue (but Akismet catches them):
!!!
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Posted by Tess | January 25, 2010, 01:07Hello there,
Thanks for publishing another valuable post. The contribution you make to our community is a huge one and I appreciate it. I’ve been popping in and reading posts as frequently as I can and regretting that my memory isn’t as keen as I wish it was.
I do recall that we could remove timestamps previous to 2.7 and I think your “decorative element” idea is a clever work around.
Thinking well of you always,
Your friend,
TT
Posted by timethief | January 30, 2010, 02:39Hi tt, thanks for your kind words, please quit the make-others-blush thing!
To me the time stamp is an insignificant detail, so I don’t think highly of this post, but whatever workarounds I come up with, I publish them just in case (actually even this tiny thing has been asked in the forum).
Posted by Panos | January 30, 2010, 15:30This is useful. I have wondered about removin time stamps for a while.
[Username link removed – P.]
Posted by OldPostageStamps | May 4, 2010, 18:17By removing the time do you risk not updating your blog as much?
[Username link removed – P.]
Posted by Financial Spread Betting | May 5, 2010, 18:41@FSB: The post suggests a workaround for eliminating the time stamp, not the date stamp.
Or maybe I’m misunderstanding your question.
(Or maybe it isn’t a question at all.)
Posted by Panos | May 5, 2010, 19:46I thought you might like to know that you can change the time to appear as a space or a non-breaking space using the method you described to include the symbols. The numbers to use are either 32 or 160. This is theme dependant though. In my test using Sandbox 1.6.1 the theme automatically includes an en-dash after the date so this will still appear. It also means when viewing an individual post it will say something like “posted on May 16, 2010 at , filed under…” which doesn’t make much sense but this isn’t the case for all themes.
Hope this is helpful to some of your readers.
Posted by Luke Hall | May 16, 2010, 19:53Hi Luke and welcome here! Yes you’re right – I had already seen your relevant reply in the forum, and I’ll incorporate this in the post somehow, if you don’t mind.
Posted by Panos | May 17, 2010, 02:22