I'm in the process of building a new site using WP. The test site is at http://www.zims.com/blog/
It's using a slightly modified (mainly to include various plug-ins) version of the default theme.
I've installed Dunstan's Time of Day plugin (the latest version updated for 1.5 htpp://www.ifelse.co.uk/archives/2005/02/20/new-release-of-time-of-day-plugin/).
The code of included in my index.php is:
'<small><?php the_time() ?> on <?php the_date() ?> <!-- by <?php the_author() ?> --></small>'
If you want to see where I've included this take a look at the source for htpp://www.zims.com/wpindex.txt.
Anyway the code seems to work fine for the top most post of any given day, however for subsequent posts on the same day it just shows the time without the date.