3.7 introduced automatic updates for security releases.
If you're running 3.9 at the moment, you're doing it wrong. Latest release is 3.9.1 - update now!
"But I'm scared I might break something" WordPress is extremely backwards compatible, if things are breaking every time you update then you have a bigger problem.
Take care when installing plugins
Don't go installing all the plugins
Keep your plugins up to date - plugin authors release security updates too.
Check feedback for the plugin - lots of reviews & 5 stars is a good indicator
Deactivate (and remove) any plugins you are not using.
Same is true for themes too.
Pick a good host
Does your host tell you to set permissions to 777?
Are they proactive against security risks?
Do they blog about security and send information?
Are they responsive on social networks?
Secure your environment
Use SFTP over FTP
Disable file editing in WP
Use SSL
Add .htaccess rules to lockdown files & folders
Check for malware (changed files)
Backup your site
Secure your code
Check permissions before performing action current_user_can('edit_posts')
Sanitize all user inputs to prevent SQL injection sanitize_text_field( $_POST['title'] );
Escape data to protect the end user from XSS esc_html( $title );
Use nonces to prevent Cross Site Request Forgery (CSRF) wp_create_nonce()
Security through obscurity.
Rename 'admin' username to something else
Change table prefix from 'wp_'
Lock down folders by .htaccess
Limit wp-admin by IP address
False economy?
Removing WP Version
Change location of wp-content
You can run but you can't hide
Use two factor authentication
There are three types of authentication widely used today