It's impossible to say precisely what Google or Bing/Yahoo use to decide how a website ranks in their search results. And if it was a knowable concept, everyone would do the same thing, and then everyone would rank the same, and there would be no way to sort websites according to any order or preference.
When Google started out, links were the major way for them to see how relevant a site was. (Incidentally, I just found this out while reading on this topic that Google's PageRank was named after Larry Page). So people started gaming this by setting up lots of websites with links to their own properties. These link farms are more easily setup using virtual servers.
Over time, hosting services used this "bad neighborhood" concept, along with subnet masks to market more hosting packages to users. The idea was that if Google could not tell if two websites were run by the same person you could generate more "link juice" by creating many sites.
Google has outright refuted that they factor in virtual hosting as part of their ranking algorithm. Because webmasters can easily take advantage of dedicated IPs, it doesn't really make much sense to me that they would care much about virtual hosting. Google is likely using other more reliable signals to try and identify someone creating artificial popularity on the web. For example, I can imagine a whole bunch of links showing up really quickly or a whole bunch of newborn websites showing up suddenly being things that raise flags to a search engine.
There is an unrelated argument for using a dedicated IP however: you cannot take advantage of SSL with virtual hosting like you can with a dedicated IP. So if you need security around data passing back and forth between you and your customers, you are likely going to want a dedicated IP.