Welcome to the forums,
If you listed your domain we could check mx records for you - or you can do a "dig mx domain.com"
Can you telnet to port 25 on that box? (from the outside - not any boxes on your lan)
If not: firewall or even your hosting provider blocking port 25?
Do a tail -f /var/log/zimbra.log do you see the connection attempts? what are the errors there?
-check the queue's
If that appears ok, then tail -f /opt/zimbra/logs/mailbox.log do you see the mail showing up there?
If not, the next question would be in regards to your dns setup...does this box have both a private & public ip?
Split DNS - ZimbraWiki /blog/archives/2007/06/making_zimbra_bind_work_together_1.html