The delete function is available for all standard users in each document list.
But this is only a "soft" delete. The right to permanently delete is only available to administrators from within the "Deleted Documents" view. Standard users can use this view to locate documents they have deleted and restore if necessary.
Users cannot delete (or edit) emails and documents when they are in Co-edit, being edited by another user or have have certain workflow states. Refer to the FAQ Why can I not Edit or Delete an email or document?