Based on your particular configuration, Drupal may not proceed beyond the login screen and may persistently give you the login page even if in the backend you are logged in. This problem occurs much easily in Internet explorer and less in Firefox 1.5. You can by pass this problem by clearing you cookies before logging in after loading the first page of the site in question (This is just a troubleshooting by-pass as you cannot mandate your web users to clear cookies manually every time they login).
The problem is caused by Drupal's inability to clear the anonymous cookie and replace it with a new cookie for your logged-in session. As mentioned above, this is more prevalent in IE and does not seem to be specific to any particular operating system. The issue is very eloquently described in http://drupal.org/node/55364.
There are a number of suggested solutions and walk-arounds that can get you from a moment of proper functionality, to permanent resolution with some consequences especially regarding SEO since some solutions require not using cookies, and switching to session IDs being embedded in the URL.