How remove "username's blog" from $links

It's a matter of theming. You has to override the theme_links function.
Here you can take a look of how to do this: http://drupal.org/node/44708

md - drupalcenter.de
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http://mdwp.de

In Drupal 5.1 (maybe earlier), each of those links has its own class. Try adding this to your theme's stylesheet:

.blog_usernames_blog { display: none; }

In my theme, that still left a little bit of space. I think it has to do with the whitespace between the list items. You can hack away at the space by adding a negative margin, though there may be a better way.

.blog_usernames_blog { margin-left: -1.5em; display: none; }

Obviously this doesn't make the links disappear for old browsers without css support, but then again, people with those browsers are probably used to seeing things much uglier than a "username's blog" link.