By default, anonymous and authenticated users will not be able to see unpublished content in Drupal. The way to grant them access is slightly different in Drupal 6 and 7.
Users that are allowed to create content, will be able to see unpublished content created by themselves, but not nodes created by others. By enabling the permission 'administer nodes' in Drupal 6, you give them permission to see all unpublished content.
Note that 'administer nodes' does much more than just allowing users to see unpublished content and should be used with care. (more information on 'administer nodes')
View Unpublished Content with Views Module
The Views module allows access to view data from unpublished nodes. It has a separate filter for published / unpublished status to block access if wanted.
In Drupal 7, users are not allowed to view any unpublished content by default, not even content created by themselves. By enabling 'View own unpublished content', you grant users access to their own unpublished content.
The only way to allow users access to all unpublished content in Drupal 7 (without using a contributed module), is to enable the permission 'Bypass content access control'.