I've had a couple of GoDaddy-based domains and associated email for perhaps 1.5 years now, and everything seemed to be working like a charm until recently.
About two months ago I got word that email sent to me had bounced as undeliverable, yet other email from the same sender earlier and later was delivered normally.
More recently, my wife sent me a text message from her cell phone. It never showed up. I then did some experiments from my own cell phone. Texts from the cell to my GoDaddy email disappeared. Identical messages to my corporate email (not hosted with GoDaddy) came through fine. Interestingly, if I sent a message from the GD account to my cell and then replied back to the GD email, that reply would work. One tentative theory is that it worked because it picked up a subject line along the way, but that's unproven.
Now today I gradually became aware that I had received no email at all after about 5:00 this morning. I've sent several test messages from my corporate email to my GD email, and none have arrived safely (but see next paragraph for a sort of exception), though GD returned successful delivery messages back.
I usually use Outlook 2003 to access my GD account via POP3. As I said, nothing has arrived there since early this morning. Just for fun, I went to the Web-based version of my GD email (email.<mydomain>.com). It also showed none of the emails that should have arrived. But here's the fun part. While I had the Web-based GD email inbox open (with nothing in it) I sent an email to it from my corporate account. As soon as it left, I refreshed the Web inbox, and there was my email! It made it! When I clicked on it, though, I got an error message saying the email had been deleted, moved, or recalled. I repeated the experiment, but instead of trying to open it when I saw it arrive, I just waited a moment and refreshed my inbox, and it was gone. Either way, it appears that email gets successfully delivered and then seconds later it disappears on its own. This is in spite of white-listing the sender and even completely turning off GD's spam filtering.
I'm regretting that 10-year contract about now.
I should mention that when I was playing with the cell phone text messages, I also noticed the arrive-and-disappear syndrome, but then I got busy on something unrelated and never pursued it further until today.
I'm not aware of ever having any trouble sending email from GD to the outside world.