Hi Rachel,
I believe this topic is still hotly debated amongst many SEO punters. In my opinion, unless you have a need for a dedicated server or a dedicated IP address then it is not worth the expense.
A few areas where shared hosting could possibly impact your SEO would be where several of the sites sharing your IP address has been penalised for spamming or black hat techniques. Or if your shared hosting environment is struggling with load and is slowing your site speed. If neither of these are present then I wouldn't imagine a dedicated server or even just a dedicated IP (the two don't have to be linked - You can be on a shared hosting platform with a dedicated IP address), would give much, if any, ROI.
I wouldn't recommend you spend too much time on this issue. The expense of a dedicated IP or Dedicated Server is probably not worth your time or money.
Rather focus on the well known, well practiced and successful SEO techniques which you will find aplenty here at SEOmoz.