DB log message: login failed for user xxx
These are often spammers, but might also be malicious users who are trying to break into your site (for example, to use it to post malware, distribute files, or as an email relay). If your set of users is small and well known then you should only be worried about these messages if they are for actual accounts on your site - that would be an indication of a brute force attack.

If your site is Drupal 7 then you already have some built in protection against brute force.

Some modules that might be useful to improve the overall login security of your site. 


http://drupal.org/project/user_restrictions
http://drupal.org/project/password_policy
http://drupal.org/project/mollom - configured to show a captcha on the login page
http://drupal.org/project/tfa
http://drupal.org/project/ga_login
http://groups.drupal.org/node/235938