A dedicated IP is needed in some important cases as follows:
SSL certificate id most important in E-commerce website for accepting the credit cards, because while money transaction the date will be encrypted and transferred from the server to the customer's browser. The SSL encrypted before the HTTP header get exchanged and it used the IP address to find the particular website. So that the dedicated IP is need if you have install SSL certificated in your website.
It is used to let the visitors to download the files from server through FTP. A domain name with a dedicated IP is needed to enable it.
Shared IP is banned from your country:
Some web hosts allows the website to publish information that are related to gambling, anti-government, or porn which are forbidden by the government from some countries. They might ban the IP address of those website. If you have host your website with the same server, you cannot access your website in that country. To avoid these type of problems getting dedicated IP is the best. There are many benefits having a Dedicated IP address. Some are as follows:
Having your own Private SSL Certificate.
Accessing your website even when the domain name is inaccessible.
Running an FTP server etc....
For these reasons i have hosted my sites in http://www.9cubehosting.com/
,Linux based dedicated hosting plan. Here they have provided me 3 dedicated IP addresses.