How do I change the default WordPress e-mail ID for sent e-mail?

Add the following to your functions.php:

add_filter('wp_mail_from', 'new_mail_from');
add_filter('wp_mail_from_name', 'new_mail_from_name');

function new_mail_from($old) {
 return 'your email address';
}
function new_mail_from_name($old) {
 return 'your name or your website';
}