Overcrowding can negatively impact SEO, User Experience, and Reliability!
Perhaps the most important test is a Reverse IP Domain check
It is widely speculated by top SEO Professionals that websites on Shared IP's will not rank as high.(source)
The more websites per server, the slower your website will be.
Reliability and Website Reputation can also be affected
Head to http://www.yougetsignal.com/tools/web-sites-on-web-server/ to perform a Reverse IP Domain Check This will tell us how many websites are on the same IP. Enter your website name without the http://. If I was testing this website, I'd enter www.thewordpressdoctor.com.
If you find more than 100 websites per IP with this test, you should consider new hosting! Wordpress based websites work their best with less than 100 websites per server.
Pay Careful Attention for a Red Warning Box for Adult content. Many hosts mix adult content themed websites with standard websites. Adult websites can negatively affect your websites reputation. If you find adult content on the same ip, you should consider finding a new webhost!