WordPress has added in support for automated upgrading of minor releases. This means it will upgrade you from 3.7 to 3.7.1 without you having to do anything. But to go from 3.7.1 to 3.8 you would need to go through the normal upgrade process. We have a post about how to prevent automated updating, but what if you really like automated updating and you want it to work for major versions as well?
Updates for major versions aren't enabled by default because major versions often come with major code changes that can sometimes break sites. So before enabling this you'll want to make sure that you are using actively developed plugins and themes so you don't have any site issues. If you're confident that you won't have issues, then enabling automated updating for major versions is very simple.
Add the following line of code to your wp-config.php file
define('WP_AUTO_UPDATE_CORE', true );
Now edit your theme's functions.php file and add this line of code
add_filter( 'allow_dev_auto_core_updates', '__return_false' );
That line prevents WordPress from updating to their nightly builds which can include bugs and isn't recommended for use on production sites.
You are now setup to be updated to any new WordPress version that gets released.