I don’t know for sure how Google takes the web hosting IP into account of determining your website’s ranking position, but I’m sure they do take that in consideration, albeit not so significantly as a maker or a breaker.
Most of my sites are currently on DreamHost and every time I register a new domain, make a grand new website with original home page content and submit it to Google, I have to wait like 2 weeks to a month or so to get indexed, even after I have linked the new site from one of my most powerful pages.
For one reason or another, I decided to give it a try with another hosting company, Rackspace Cloud. I have been with them for nearly a month now and everything’s been smooth and pleasant, no downtime that I can experience of.
The most exciting part is, however, that after submitting all 3 freshly registered domains (which I’m sorry that I can’t disclose) with 3 blank home pages that are not even HTML, containing just a string text of the domain, to Google, they all got indexed in less than 3 days.
The home pages don’t even have a title and I never bothered to link to them either. Strange, but sort of understandable.
DreamHost is currently hosting like 700,000 domains. Imagine a huge city that everyone has some websites hosted by them. Google knows that your websites are with them by the IP which may very well has been used by some spammer or spamming sites before or even worse, you are currently sharing the IP with another spammer or slug dog rubbish-quality-seeking-money-quick kind of site. Even the IP itself has a clean history and is only used by fairly good sites, Google knows you are with DH by the IP range chart and because of the simple fact that a lot of sites on DH are not so good, it looks down upon you, with good reason. You can’t blame it.
However this is not to say all websites with DH are bad or worthless ones, a lot of them are very outstanding actually. Therefore, Google has thought about it and decides once a site crosses a threshold that’s determined by the content originality, update frequency and number of quality backlinks, it will let go of the fact that you are hosting in a bad neighborhood. But before your site hits that mark, it will be treated like it’s a slug dog because it is born in a spammy IP range.
You can still make wonderful things happen, but slightly more difficult.
This is not just about DreamHost. All heavily marketed cheap / affordable web hosting companies have the same problems and may pose similar SEO disadvantages to your sites, though maybe in a gentle manner. Because they are cheap, they have long since become a paradise for underprivileged short-sighted webmasters to build under-quality sucking websites.
On the contrary, if you host your sites at a premium hosting provider with your own fresh IP addresses, Google will be more likely to show love to them from the very beginning.
Anyway, this is just my theory that’s never been practically testified. But I have always held faith in the Law of Attraction: Everything that happens to you is attracted by yourself.