Some SEO Companies and Experts claim that sites with a static IP address rank higher while other SEOs claim that shared hosting is just fine, that it would be stupid for search engines to penalize shared hosting since we are running out of IP addresses and so many sites are currently using name based hosting. In Early days every host on the Internet had a unique IP address. It is usually expressed as 4 numbers from 0-255 separated by dots. An example would be 207.44.161.131. There are billions of such IP addresses possible, however, there is a finite number. An organization called ARIN hands out IP addresses in the western hemisphere while another organization handles Europe and another Asia. Those organizations noticed several years ago that we were going to eventually run out of those IP addresses because of the proliferation of web-sites. At the time, every website had it's own dedicated IP address that was associated with it's domain name. A new protocol was developed called HTTP 1.1. The new protocol allowed more than one domain/website to share the same IP address. In fact, hundreds of websites can now share the same IP address. The new type of hosting is called "name based", "shared IP", "http 1.1", etc.

Some SEOs theorize that your choice of dedicated hosting vs. shared hosting might affect your rankings. Some others claim that is ridiculous because all hosting will eventually be shared in order to preserve IP addresses. First, it is interesting to note that the number of sites using shared vs. dedicated hosting is just about half.
The second thing is that there is no trend for either Yahoo or Google that would indicate any preference for either type of site. Google might show a slight preference for static IP. Yahoo might show a slight preference for shared hosting. The net effect is null.