GoDaddy offers one with your hosting plan that works. It's pretty basic and you need to use your admin panel to set the email address for it...
https://support.godaddy.com/help/article/508/specifying-an-email-address-for-the-php-form- mailer
I've used the Formmail script from http://www.tectite.com in the past with some success on GoDaddy accounts, but no longer use GoDaddy, so I'm not sure if anything has changed there.