I've googled that and I've found many opinions on this subject, and I'm not sure, if, dedicated IP addresses actually really improve SEO? Is it that different from shared IP address (of 50-100 other sites)?
The IP address where your website is hosted has no effect on SEO.
Since we're probably only talking about Google here, I found this link about how Google's PageRank is not affected by your IP address (or more specifically, how many websites are hosted at a given IP address).
My own theory as to why this opinion has developed is because larger companies typically throw way more money at their infrastructure (networks, servers, IP address blocks, etc.) than a small business, that may need to cut corners by going with a virtually hosted solution for their website. Since these larger companies have the budget, they spend more on SEO for their websites, which results in better Page Ranks, which leads to illusion that websites on dedicated IP addresses get better Page Rank.
Addendum: In the comments, Coops brings up a good point about IP blocks that get placed on blacklists for one reason or another. I'm wondering myself if this has any effect on SEO, or just with services like SMTP and the like. Anyone have any thoughts on this?
Dedicated IP addresses have no effect on SEO as IP addresses in no way indicate anything about the content and whether or not it is relevant for a search query. A site on a shared IP that moves to a dedicated IP, or vice versa, is no better or worse because of that IP address. So the IP address won't affect the ranking of pages.
IP addresses may be used, and probably is used, as an indicator for possible TOS violations (i.e. part of a content farm, content spammer, etc). But each site/page will still be judged on its own merits as shared IP addresses are very common and to ban or penalize an IP address because one site using it is black hat is obviously bad for business (and just not smart).
It's easy for SEOs to get bogged down in the details and forget that Google's algorithm is all about relevance to the user. They desperately want anyone who searches to use Google, and to ensure that, they need to provide the most relevant results. So let's put this to the test... would a dedicated IP vs. a shared IP affect relevance to the user in any way? As far as I know, users don't know and don't care, so it's a pretty safe bet this has no impact on SEO.
It is more important for mail servers and spam than for SEO. Google will obviously assume that all sites on the group are owned and operated by one person or company. That means that if you link from one site to another it doesn't really benefit you.
I have about 15 IPs in a row, all different online ventures, and have had no problems. Plus, I think with elastic IPs and more cloud hosting its likely that it will have no weight positive or negative really soon.
In other words: don't worry about it.