Well many believe that it is a myth, and the only good use for a dedicated IP address is to host your SSL. After working on Search Engine Optimization for years I have found dedicated IP’s to be very helpful. If you run a network of sites and want to link them all together it is best to have dedicated IP’s for each. This will help stop search engines from thinking that you are trying to cheat the system by making as many pages as possible and linking them together.
Another very important use of a dedicated IP is to pin point a problem only to your site instead of having to search through perhaps hundreds of sites on a shared IP address to find a search engine error. I have heard horror stories where some shared IP’s are banned or penalized by search engines, because they contain too many problem sites. A dedicated IP and a good host will get rid of that potential problem.
The main reason why I think a dedicated IP really helps in search engine placement is by just looking at the top sites on the major search engines. Most of the time for the top keywords the first 20 or more sites all have dedicated IP’s. Coincident or not, its enough for me to continue to use dedicated IP’s.