I've had sites that use both shared and fixed IPs, and seen no impact one way or the other. Personally, I've always felt this was a bit of a myth.
The only thing I could see that would impact
SEO is if an IP was previously blacklisted for negative behaviour.
The only advantages to a static IP are the non-
SEO ones khurramali suggested.
The other problem with static IPs is that they are limited to 255 to the 4th power. That seems like a big number, but consider the number of domains being registered, as well as individual IPs being assigned to internet connections, and it's really not all that much. And by that logic, someone who hosts from home on a static IP would gain a competitive advantage over someone who hosts on a reliable host with a shared IP. I can't see SEs not recognizing this and accounting for it as a result.