Allow WordPress to update itself without using FTP

Quick and simple, if you want to avoid putting FTP credentials into WordPress every time that you perform an update add this to your wp-config.php file somewhere before the magic stop line ("That's all, stop editing!")

define('FS_METHOD', 'direct');

More from the codex here

You might also need to mess with permissions, the below will give everyone and their grandmother permissions to write. However, you probably want to use 755 or something else instead of 777. If you have any questions about this please do not ask me but instead check the codex and your host.

chmod 777 wp-content/
chmod 777 wp-content/plugins/
chmod 777 wp-content/upgrade/