i believe with the given "Leave a Reply" fields, it goes to my e-mail instead and not posted automatically.
The form you describe is the comment form visitors who are not WordPress.com users or logged out users see on your posts, unless you have turned off commenting. The comment form does not send an email to you, unless you have set up email notifications in your Discussion settings. If you have set up notifications, you will receive an email notification each time a new comment is posted regardless of whether a commenter is logged in or not. http://en.support.wordpress.com/settings/discussion-settings/#e-mail-me-whenever
If you want comments to appear immediately without your intervention, then do not check either of the boxes under Discussion Settings> Before A Comment Appears http://en.support.wordpress.com/settings/discussion-settings/#before-a-comment-appears
If you wish to allow anonymous comments, then in Discussions Settings>Other Settings, uncheck the boxes "Comment author must fill out name and e-mail" and "Users must be registered and logged in to comment".
As timethief mentioned above, by not moderating comments, you are letting yourself open for potential comment spam, or at least those comments that Akismet does not catch as spam.