Some bloggers and SEO companies claim that dedicated IP addresses are better for SEO since Google prefers sites that don’t share IPs. Though, this isn’t proven.
There may be a small speed difference between shared hosting and other types of hosting, but this is not a direct relationship since shared hosting accounts can have dedicated IP addresses. Server speed can still vary depending on many other factors.
There are also claims that sites with the same IP address are less trusted. This isn’t proven either.
Most of these arguments are moot, because Google has said it will be using SSL certificates as a factor in its search engine rankings. Since you need a dedicated IP for an SSL certificate, there’s now a proven, albeit secondary, SEO benefit to having a dedicated IP.