When adding a new user, you have the choice of assigning them as a Administrator, Editor, Author, Contributor or Subscriber. Below is a simple chart to show you what each user role is allowed to do.
Note: Ryan Duff pointed out something that I should clarify here.
Under delete any published posts – for an Author, this means you can delete only your posts
Under edit and delete posts – for both an Author and a Contributor, they can, again, only delete their own posts.
You can follow Ryan on twitter at @ryanduff. Thanks Ryan!