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);