GoDaddy is currently experiencing a major systems failure which is causing DNS lookups on thousands of customer domains to fail.
GoDaddy’s DNS Servers Go Down, Along With Thousands of Sites
This is causing email deliveries to affected domains to fail. We're seeing thousands of emails queuing up in our outbound SMTP servers. The emails will be delivered once GoDaddy gets back online.
If delivery to a domain configured on your account is failing, you can force our system to bypass MX record lookups and assume internal delivery. Log into the Account Manager and select 'Domain -> Options' from the top menu. Uncheck 'Use DNS MX records for routing outbound mail to this domain' and click 'Save Options'.