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Since Drupal 6, Update Status module has been included in the core download.
This module makes your Drupal website connect to drupal.org so that it can check for newer versions of Drupal and of core and contributed themes. However, some hosts do not allow the server to make outgoing connections, and this can cause the admin pages to "hang". This can also be a problem if you are running Drupal on your own computer, for example, behind a corporate firewall/proxy. There are also reports of this problem when using Vista/WAMP.
The Update Status module is enabled by default in Drupal 6 (if you leave the checkbox "Update notifications: Check for updates automatically - With this option enabled, Drupal will notify you when new releases are available..." checked).
To turn it off, visit the modules admin page (Admin -> Site building -> Modules) at path /admin/build/modules. If you can't reach that page then you will need to edit the database manually: see http://drupal.org/node/157632.
There are open issues to improve the behaviour of Drupal in this situation [need references]...