Wordpress - How can I stop WordPress from prompting me to enter FTP information when doing updates?

If you edit your wp-config.php file you can preload these FTP settings as constants read by WordPress. Keep in mind, on a shared host, you should be mindful of possible security implications. See Editing wp-config.php for more information.

Your settings will vary, but these work for me and my hosting setup. I've included some of the unused constants, prefixed:

define('FS_METHOD', 'direct');
define('FTP_BASE', '/usr/home/username/public_html/my-site.example.com/wordpress/');
define('FTP_CONTENT_DIR', '/usr/home/username/public_html/my-site.example.com/wordpress/wp-content/');
define('FTP_PLUGIN_DIR ', '/usr/home/username/public_html/my-site.example.com/wordpress/wp-content/plugins/');
// define('FTP_PUBKEY', '/home/username/.ssh/id_rsa.pub');
// define('FTP_PRIKEY', '/home/username/.ssh/id_rsa');
define('FTP_USER', 'my-ftp-username');
define('FTP_PASS', 'my-ftp-password');
define('FTP_HOST', 'ftp.my-site.example.com');
// define('FTP_SSL', false);

Check your file ownership. When the user that apache runs as can write to the wordpress directories, then the integrated upgrade process all just works without ftp. The FTP credentials are for if the web server doesn't have the right priviledges on your files, then wordpress prompts you for your FTP details, and attempts to use those to FTP back to the same server it is on to be able to write the files it needs.

It seems that not only does WordPress check if the directories are writable, but it checks if the Apache user OWNS the directories (or at least, if the Apache user owns the temporary file it creates). Observe these lines of code at /wp-admin/includes/file.php: get_filesystem_method():

if ( $temp_handle ) {
    if ( getmyuid() == @fileowner($temp_file_name) )
        $method = 'direct';
    @fclose($temp_handle);
    @unlink($temp_file_name);
}

So, a quick solution will be to issue this command and give ownership of the whole Wordpress installation to Apache:

sudo chown -R www-data wordpress/

Where www-data is the Apache user, and of course wordpress is your WordPress installation folder.

I have further documented my solution here: https://ardeearam.wordpress.com/2013/02/03/solved-wordpress-asking-for-ftp-credentials-when-upgrading/