NOTE: I have only used their Virtual Dedicated Servers and SSL certificates.
First the SSL certificates. They sell chained root certificates, which can cause problems with many browsers. I use Internet Explorer 6 and FireFox 1.5. Both of these had problems with the "Starter" SSL certificate I purchased, prompting me to accept the certificate. See http://www.rapidssl.com/ssl-certificate-support/ssl-faq.htm for an explanation of chained root certificates. I bought a certificate from rapidssl.com and have not had one problem yet.
As for GoDaddy's virtual dedicated server hosting... I tried a Windows VDS and cancelled it inside a week because it was unacceptably slow, I suspect due to the limited memory. My Linux (Fedora Core) VDS has performed very well generally, and my customers and I were happy with their service for the first couple of months, but have had some recent problems.
I personally have several domains, most of which forward email to a single remote (on another server) account (for a consolidated view of all my email). This forwarding caused the outgoing mail server to hit the 1000 email per day per server (NOTE: not per domain, but per server) to be reached very quickly, causing all of my customers on my VDS to lose email sending capabilities until the following midnight. Plus, it queued all email up until midnight, and those began to get to the point that it took 3-4 days to send an email because the queue had that many messages. It would hit midnight and forward the first 1000 emails in the queue, hit the limit and wait 24 hours to send the next 1000.
I requested an increase in this 1000 limit, and to have it limit per domain so it would only affect me, not my customers. They raised my limit, but on the wrong IP address (I requested 3 for the VDS). On the next call, they realized it was on the wrong IP address and said they'd adjust the correct one. I asked for a phone call when it was done, but they said they could only notify me by email. I never received the email. I continued to get "over your 1000/day message limit" messages and complaints from my customers.
On another note, I have had a huge influx of "bounce" messages and people requesting to be removed from whatever list they got some spam from. When looking at the source of the message (and the fact that my VDS has relaying turned off), it was spoofed, meaning someone sent it to them from somewhere else using my domain as the From address so I'd get the bounce message. This is probably purely coincidental that it started about two weeks after signing up with GoDaddy, but I still wonder.
I am currently in the process of moving all of my services and all of my customers to a new hosting company.
I am very disappointed because their prices are great for virtual dedicated servers, the setup was acceptably quick, and the Plesk control panel was great to use. Every host seems to have one thing that's a deal breaker. Either it's the 1000 per day email limit, or they don't use the control panel you like, or they support POP3 but not IMAP4, or any number of other issues.