Do I need a dedicated IP Address?
Short answer: No
I need a Dedicated IP address so that visitors using older browsers can view my website
This is only the case for very old web browsers (Internet Explorer 6-8) on very old operating systems (Windows XP) because they don’t support a feature called SNI (Server Name Indication).
SNI solved the problem by allowing SSL Certificates to operate on a shared IP Address, meaning that dedicated IP Addresses are no longer required.
I need a dedicated IP address to help improve my SEO ranking
This one was actually debunked a long time ago by Google’s Director of Technology. You can read the interview in full here. Even today in Google’s webmaster guidelines there is no mention of anything to suggest that having a Dedicated IP will in any way improve your SEO ranking.
I need a dedicated IP address so that my email delivery is not affected by other users on the server
All of our shared hosting servers actually route mail through a Spam Experts Outbound Spam Filter. This means that even with a Dedicated IP address, the IP address that is actually sending the email is the address of our Spam Filter (this cannot be changed on a per-user level). The spam filter is there for the very purpose of ensuring the IP reputation stays positive and email deliverability is always at its best.