I am sure you know your neighbors where you live, but what about the neighbors to your website where it resides? This may sound like a weird question and many will wonder what it matter who is hosted on a server with them. Most any business owner knows that if you have the best website available for your market nobody will use it if they cannot find it. For these users to find you, you must appear in the major search engines for the terms, which are relevant to your site. So what does your server neighbors possibly have to do with this?
Search engines do not like sites, which try to trick them into listing sites in searches they are not truly relevant for. So if you place your site on a shared hosting service you can potentially be guilty by association if those who share your space with you do not follow the general rules search engines prefer sites follow. The only way to ensure your site is not penalized for what other sites on a shared hosting plan are doing is by going with a dedicated hosting plan. At one time dedicated web hosting was much more expensive, but now it is quite easy to fine affordable dedicated hosting for your site.