Do you know that Google thinks shared hosting is an acceptable form of web hosting ? You do not need to move to a dedicated server for SEO purposes. But make sure that you are with a good hosting company which will make sure that websites are not overloaded.
Google ranks each website based on its value, not based on other websites on the shared hosting server. If you have a bad neighbour, there is no need to worry about it.
That is certainly a relief to people who are not planning to use a VPS or a dedicated server